Exhibit 10.8

[], 2021

Peridot Acquisition Corp. III
2229 San Felipe Street, Suite 1450
Houston, TX 77019

Ladies and Gentlemen:

This letter (this “Letter Agreement”) is being delivered to you in accordance with the Underwriting Agreement (the “Underwriting Agreement”), entered into by and among Peridot Acquisition Corp. III, a Cayman Islands exempted company (the “Company”), BofA Securities, Inc. and J.P. Morgan Securities LLC, as representatives (the “Representatives”) of the several underwriters (the “Underwriters”), relating to an underwritten initial public offering (the “Public Offering”) of [] of the Company’s units, including up to [] additional units that may be purchased to cover over-allotments, if any, (collectively, the “Units”), each comprised of one Class A ordinary share of the Company, par value $0.0001 per share (the “Ordinary Shares”), and one-[] of one redeemable warrant (each whole warrant, a “Warrant”). Each Warrant entitles the holder thereof to purchase one Ordinary Share at a price of $11.50 per Ordinary Share, subject to adjustment. The Units shall be sold in the Public Offering pursuant to the registration statement on Form S-l (File No. 333-[]) including the prospectus contained therein (the “Prospectus”), filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”), and the Company has applied to have the Units listed on the New York Stock Exchange. Certain capitalized terms used herein are defined in paragraph 1 hereof.

In order to induce the Company and the Underwriters to enter into the Underwriting Agreement and to proceed with the Public Offering and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, Peridot Acquisition Sponsor III, LLC (the “Sponsor”), and each of the undersigned individuals, each of whom is a member of the Company’s board of directors (the “Board”) and/or management team (each, an “Insider” and, collectively, the “Insiders”), hereby agrees with the Company as follows:

1.Definitions. As used herein, (i) “Business Combination” shall mean a merger, amalgamation, share exchange, asset acquisition, share purchase, reorganization or similar business combination with one or more businesses or entities; (ii) “Founder Shares” shall mean the [      ] Class B ordinary shares of the Company, par value $0.0001 per share, outstanding (or [] shares if the over-allotment option is not exercised in full by the Underwriters), initially held by the Sponsor, the Company’s independent directors and any other holder prior to the consummation of the Public Offering; (iii) “Private Placement Warrants” shall mean the warrants to purchase up to [         ] Ordinary Shares (or [      ] Ordinary Shares if the over-allotment option is exercised in full by the Underwriters) that will be acquired by the Sponsor for an aggregate purchase price of $[     ] in the aggregate (or up to $[] in the aggregate if the over-allotment option is exercised in full by the Underwriters), or $[] per Private Placement Warrant, in a private placement that shall close simultaneously with the consummation of the Public Offering (including the Ordinary Shares issuable upon conversion thereof); (iv)

“Public Shareholders” shall mean the holders of Ordinary Shares included in the Units issued in the Public Offering; (v) “Public Shares” shall mean the Ordinary Shares included in the Units issued in the Public Offering; (vi) “Trust Account” shall mean the trust account into which a portion of the net proceeds of the Public Offering and the sale of the Private Placement Warrants shall be deposited; (vii) “Transfer” shall mean the (a) sale of, offer to sell, contract or agreement to sell, hypothecate, pledge, grant of any option to purchase or otherwise dispose of or agreement to dispose of, directly or indirectly, or the establishment or increase of a put equivalent position or liquidation with respect to or decrease of a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the rules and regulations of the Commission promulgated thereunder with respect to, any security, (a) entry into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any security, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise or (a) public announcement of any intention to effect any transaction specified in clauses (a) or (b); and (viii) “Charter” shall mean the Company’s amended and restated memorandum and articles of association, as the same may be amended from time to time.

2.Representations and Warranties.

(a)The Sponsor and each Insider represents and warrants to the Company that it, she or he has the full right and power, without violating any agreement to which it, she or he is bound (including, without limitation, any non-competition or non-solicitation agreement with any employer or former employer), to enter into this Letter Agreement, as applicable, and to serve as an officer of the Company and/or a director on the Company’s Board, as applicable.

(b)Each Insider represents and warrants that such Insider’s biographical information furnished to the Company and the Representatives (including any such information included in the Prospectus) is true and accurate in all respects and does not omit any material information with respect to such Insider’s background and contains all of the information required to be disclosed pursuant to Item 401 of Regulation S-K, promulgated under the Securities Act of 1933, as amended (the “Securities Act”).

3.Business Combination Vote. It is acknowledged and agreed that the Company shall not enter into a definitive agreement regarding a proposed initial Business Combination without the prior consent of the Sponsor. The Sponsor and each Insider hereby agrees that if the Company seeks shareholder approval of a proposed initial Business Combination, then in connection with such proposed initial Business Combination, it, she or he, as applicable, shall vote all Founder Shares and any Public Shares held by it, her or him, as applicable, in favor of such proposed initial Business Combination (including any proposals recommended by the Board in connection with such proposed initial Business Combination) and not redeem any Public Shares held by it, her or him, as applicable, in connection with such shareholder approval.

4.Failure to Consummate a Business Combination; Trust Account Waiver.

(a)The Sponsor and each Insider hereby agrees that in the event that the Company fails to consummate its initial Business Combination within the time period set forth in the Charter, the Sponsor and each Insider shall take all reasonable steps to cause the Company to

(i) cease all operations except for the purpose of winding up; (i) as promptly as reasonably possible but not more than ten (10) business days thereafter, redeem 100% of the Public Shares, at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account and not previously released to the Company to pay income taxes (less up to $100,000 of interest to pay dissolution expenses), divided by the number of then outstanding Public Shares, which redemption will completely extinguish the Public Shareholders’ rights as shareholders of the Company (including the right to receive further liquidation distributions, if any), subject to applicable law; and (i) as promptly as reasonably possible following such redemption, subject to the approval of the Company’s remaining shareholders and the Board, liquidate and dissolve, subject in each case to the Company’s obligations under Cayman Islands law to provide for claims of creditors and in all cases subject to the other requirements of applicable law. The Sponsor and each Insider hereby agrees not to propose any amendment to the Charter (i) in a manner that would affect the substance or timing of the Company’s obligation to redeem 100% of the Public Shares if the Company does not complete an initial Business Combination within the required time period set forth in the Charter or (i) with respect to any other provision relating to the rights of Public Shareholders unless the Company provides its Public Shareholders with the opportunity to redeem their Public Shares upon approval of any such amendment at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account and not previously released to the Company to pay its income taxes, if any, divided by the number of then-outstanding Public Shares.

(b)Pursuant to the Charter, the Sponsor and each Insider (i) have no right, title, interest or claim of any kind in or to any monies held in the Trust Account or any other asset of the Company as a result of any liquidation of the Company with respect to the Founder Shares and (ii) are not entitled to redemption rights with respect to the Founder Shares. The Sponsor and each Insider hereby waives, solely with respect to any Public Shares held by it, her or him, as applicable, any redemption rights it, she or he may have in connection with the consummation of an initial Business Combination, including, without limitation, any such rights available in the context of a shareholder vote to approve such initial Business Combination or a shareholder vote to approve an amendment to the Charter (i) that would affect the substance or timing of the Company’s obligation to redeem 100% of the Public Shares if the Company has not consummated an initial Business Combination within the time period set forth in the Charter or (i) with respect to any provision relating to the rights of Public Shareholders.

5.Lock-up; Transfer Restrictions.

(a)The Sponsor and each Insider hereby agrees that they shall not Transfer any Founder Shares or Ordinary Shares issuable upon conversion of the Founder Shares held by it, her or him (the “Founder Shares Lock-up”), until the earlier of (i) one (1) year after the completion of an initial Business Combination and (ii) following the completion of an initial Business Combination, the date on which the Company completes a liquidation, merger, share exchange or other similar transaction that results in all of the Company’s shareholders having the right to exchange their Ordinary Shares for cash, securities or other property (the “Founder Shares Lock-up Period”). Notwithstanding the foregoing, if, subsequent to a Business Combination, the closing price of the Ordinary Shares equals or exceeds $12.00 per share (as adjusted for share sub-divisions, share capitalizations, share consolidations, reorganizations, recapitalizations and the

like) for any twenty (20) trading days within any thirty (30)-trading day period commencing at least one-hundred and fifty (150) days after the consummation of the Company’s initial Business Combination, the Founder Shares shall be released from the Founder Shares Lock-up.

(b)Subject to the exceptions set forth herein, the Sponsor and each Insider hereby agrees that he, she or it shall not effectuate any Transfer of Private Placement Warrants or Ordinary Shares underlying such Warrants held by it, her or him until thirty (30) days after the completion of an initial Business Combination.

(c)Notwithstanding the provisions set forth in paragraphs 5(a) and (b), Transfers of the Founder Shares, Private Placement Warrants and Ordinary Shares issued or issuable upon the exercise or conversion of the Private Placement Warrants or the Founder Shares and that are held by the Sponsor, any Insider or any of their permitted transferees, as applicable,  are permitted (i) to the Company’s officers or directors, any affiliates or family members of any of the Company’s officers or directors, any members or partners of the Sponsor or their respective affiliates, any affiliates of the Sponsor, or any employees of such affiliates; (ii) in the case of an individual, by gift to a member of one of the individual’s immediate family or to a trust, the beneficiary of which is a member of the individual’s immediate family, an affiliate of such person or to a charitable organization; (iii) in the case of an individual, by virtue of laws of descent and distribution upon death of the individual; (iv) in the case of an individual, pursuant to a qualified domestic relations order; (v) by private sales or transfers made in connection with any forward purchase agreement, backstop agreement or similar arrangement or in connection with the consummation of a Business Combination at prices no greater than the price at which the Founder Shares, Private Placement Warrants or Ordinary Shares, as applicable, were originally purchased; (vi) by virtue of the Sponsor’s organizational documents upon liquidation or dissolution of the Sponsor; (vii) to the Company for no value for cancellation in connection with the consummation of an initial Business Combination; (viii) in the event of the Company’s liquidation prior to the completion of an initial Business Combination; or (ix) in the event of the Company’s completion of a liquidation, merger, amalgamation, share exchange or other similar transaction which results in all of the Company’s Public Shareholders having the right to exchange their Ordinary Shares for cash, securities or other property subsequent to the completion of an initial Business Combination; provided, however, that in the case of clauses (i) through (vi) these permitted transferees must enter into a written agreement agreeing to be bound by these Transfer restrictions.

(d)During the period commencing on the effective date of the Underwriting Agreement and ending one-hundred and eighty (180) days after such date, the Sponsor and each Insider shall not, without the prior written consent of the Representatives, (i) Transfer any Units, Ordinary Shares, Founder Shares, Warrants or any other securities convertible into, or exercisable or exchangeable for, Ordinary Shares held by it, her or him, as applicable, provided, however, that the foregoing shall not apply Transfers to the Sponsor by the Insiders, (ii) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any Units, Ordinary Shares, Founder Shares, Warrants or any other securities convertible into, or exercisable, or exchangeable for, Ordinary Shares owned by it, her or him, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise or (iii) publicly announce any intention to effect any transaction specified in clauses (i) or (ii). If the undersigned Insider is an officer or director of the Company, the undersigned further agrees that the forgoing restrictions shall be equally applicable to any issuer-directed Units that the

undersigned may purchase in the Public Offering. Each of the Insiders and the Sponsor acknowledges and agrees that, prior to the effective date of any release or waiver of the restrictions set forth in this paragraph 5, the Company shall announce the impending release or waiver by press release through a major news service at least two (2) business days before the effective date of the release or waiver. Any release or waiver granted shall only be effective two (2) business days after the publication date of such press release. The provisions of this paragraph 5 will not apply if (a) the release or waiver is effected solely to permit a Transfer of securities that is not reportable in accordance with Section 16 of the Exchange Act and (b) the transferee has agreed in writing to be bound by the same terms described in this Letter Agreement to the extent and for the duration that such terms remain in effect at the time of the Transfer.

6.Remedies. The Sponsor and each Insider hereby agrees and acknowledges that (i) each of the Underwriters and the Company would be irreparably injured in the event of a breach by the Sponsor or such Insider of its, her or his obligations, as applicable under paragraphs 3, 4, 5(c), 7, 10 and 11, (i) monetary damages may not be an adequate remedy for such breach and (i) the non-breaching party shall be entitled to injunctive relief, in addition to any other remedy that such party may have in law or in equity, in the event of such breach.

7.Payments by the Company. Except as disclosed in the Prospectus, neither the Sponsor, the Insiders nor their respective affiliates shall receive from the Company any finder’s fee, reimbursement, consulting fee, monies in respect of any repayment of a loan or other compensation prior to, or in connection with any services rendered in order to effectuate the consummation of the Company’s initial Business Combination (regardless of the type of transaction that it is). However, such persons may receive the following payments, none of which will be made from the proceeds held in the Trust Account prior to the completion of the initial Business Combination: (i) repayment of a loan of up to $300,000 made to the Company by the Sponsor, pursuant to a Promissory Note, dated March 23, 2021; (ii) payment of an aggregate of up to $40,000 per month, to [       ] or any permitted assignee thereof, as reimbursement to it for making available to the Company office space, secretarial support and administrative support, pursuant to an Administrative Services Agreement dated [       ], 2021; (iii) reimbursement for any reasonable out-of-pocket expenses related to identifying, investigating, negotiating and consummating an initial Business Combination; and (iv) repayment of loans, if any, and on such terms as to be determined by the Company from time to time, made by the Sponsor or an affiliate of the Sponsor or certain of the Company’s officers and directors to finance transaction costs in connection with an intended initial Business Combination, provided that if the Company does not consummate an initial Business Combination, a portion of the working capital held outside the Trust Account may be used by the Company to repay such loaned amounts so long as no proceeds from the Trust Account are used for such repayment. Up to $[1,500,000] of such loans may be convertible into Warrants at a price of $[] per Warrant at the option of the lender. Such Warrants shall be identical to the Private Placement Warrants, including as to exercise price, exercisability, exercise period and restrictions on transfer.

8.Directors’ and Officers’ Liability Insurance.

(a)To the fullest extent permitted by applicable law, the Company hereby agrees to defend, indemnify, hold harmless and exonerate (including the advancement of expenses to the fullest extent permitted by applicable law) the Sponsor and its members (present and former),

managers and affiliates and their respective present and former officers and directors (each, a “Sponsor Indemnitee”) from any and all costs, fees, expenses, judgments, liabilities, fines, penalties, reasonable attorneys’ fees and amounts paid in settlement (including all interest, assessments and other charges paid or payable in connection with or in respect of such costs, fees, expenses, judgments, liabilities, fines, penalties and amounts paid in settlement) actually, and reasonably, incurred by a Sponsor Indemnitee or on a Sponsor Indemnitee’s behalf in connection with any threatened, pending or completed action, suit, arbitration, mediation, alternate dispute resolution mechanism, investigation, inquiry, hearing or any other actual, threatened or completed proceeding instituted by the Company or any third party, whether civil, criminal, administrative or investigative in nature, in respect of any investment opportunities sourced by a Sponsor Indemnitee for the Company or any liability arising with respect to a Sponsor Indemnitee’s activities in connection with the affairs of the Company (in each case to the extent that such indemnification, hold harmless and exoneration obligations with respect to such matters are not expressly covered by a separate written agreement between the Company and the applicable Sponsor Indemnitee); provided that in no event shall a Sponsor Indemnitee be entitled to be indemnified or held harmless hereunder in respect of any costs, fees, expenses, judgments, liabilities, fines, penalties and amounts paid in settlement (if any) that Sponsor Indemnitee may incur by reason of such person’s own actual fraud or intentional misconduct; provided further, for the avoidance of doubt, that under no circumstance shall a Sponsor Indemnitee have a claim to any monies or assets held in the Trust Account, and the Company shall not be permitted to procure monies or assets held in the Trust Account for the satisfaction of its obligations to any Sponsor Indemnitee in respect of the indemnification provided herein. The Sponsor Indemnitees shall be third party beneficiaries of this paragraph 8.  

(b)The Company will maintain an insurance policy or policies providing directors’ and officers’ liability insurance, and the Insiders shall be covered by such policy or policies, in accordance with its or their terms, to the maximum extent of the coverage available for any of the Company’s directors or officers.

9.Termination. This Letter Agreement shall terminate on the earlier of (i) the expiration of the Founder Shares Lock-up Period or (i) the liquidation of the Company, provided, however, that this Letter Agreement shall earlier terminate in the event that the Public Offering is not consummated and closed by [], 2021, provided further that paragraph 10 of this Letter Agreement shall survive such termination and/or liquidation.

10.Indemnification. In the event of the liquidation of the Trust Account upon the failure of the Company to consummate its initial Business Combination within the time period set forth in the Charter, the Sponsor (which for purposes of clarification shall not extend to any officer, member or manager of the Sponsor) agrees to indemnify and hold harmless the Company against any and all loss, liability, claim, damage and expense whatsoever (including, but not limited to, any and all legal or other expenses reasonably incurred in investigating, preparing or defending against any litigation, whether pending or threatened, or any claim whatsoever) to which the Company may become subject as a result of any claim by (i) any third party for services rendered or products sold to the Company (except for the Company’s independent public accountants) or (i) a prospective target business with which the Company has entered into a letter of intent, confidentiality or other similar agreement or Business Combination agreement (a “Target”); provided, however, that such indemnification of the Company by the Sponsor shall apply only to

the extent necessary to ensure that such claims by a third party for services rendered (other than the Company’s independent public accountants) or products sold to the Company or a Target do not reduce the amount of funds in the Trust Account to below the lesser of (A) $10.00 per Public Share and (B) the actual amount per Public Share held in the Trust Account due to reductions in the value of the trust assets as of the date of the liquidation of the Trust Account, in each case including interest earned on the funds held in the Trust Account and not previously released to the Company to pay income taxes (less up to $100,000 of interest to pay dissolution expenses), except as to any claims by a third party or Target that executed an agreement waiving claims against all rights to seek access to the Trust Account (whether or not such agreement is enforceable). In the event that any such executed waiver is deemed to be unenforceable against such third party, the Sponsor shall not be responsible for any liability as a result of any such third party claims. Notwithstanding any of the foregoing, such indemnification of the Company by the Sponsor shall not apply as to any claims under the Company’s obligation to indemnify the Underwriters against certain liabilities, including liabilities under the Securities Act. The Sponsor shall have the right to defend against any such claim with counsel of its choice reasonably satisfactory to the Company if, within fifteen days (15) days following written receipt of notice of the claim to the Sponsor, the Sponsor notifies the Company in writing that it shall undertake such defense.

11.Forfeiture of Founder Shares. To the extent that the Underwriters do not exercise their over-allotment option to purchase additional Units in full within forty-five (45) days from the date of the Prospectus (as further described therein), the Sponsor agrees to automatically surrender to the Company for no consideration and for cancellation at no cost, an aggregate number of Founder Shares so that the number of Founder Shares will equal 20% of the sum of the total number of Ordinary Shares and Founder Shares outstanding at such time. The Sponsor and each Insider further agrees that to the extent that the size of the Public Offering is increased or decreased, the Company will effect a share capitalization or a share surrender, as applicable, with respect to the Founder Shares immediately prior to the consummation of the Public Offering in such amount as to maintain the number of Founder Shares at 20% of the sum of the total number of Ordinary Shares and Founder Shares outstanding at such time.

12.Entire Agreement. This Letter Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby. This Letter Agreement may not be changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision, except by a written instrument executed by all parties hereto.

13.Assignment. No party hereto may assign either this Letter Agreement or any of its rights, interests, or obligations hereunder without the prior written consent of the other parties. Any purported assignment in violation of this paragraph 13 shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee. This Letter Agreement shall be binding on the Sponsor, each of the Insiders and each of their respective successors, heirs, personal representatives and assigns and permitted transferees.

14.Counterparts. This Letter Agreement may be executed in any number of original or facsimile counterparts, and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

15.Effect of Headings. The paragraph headings herein are for convenience only and are not part of this Letter Agreement and shall not affect the interpretation thereof.

16.Severability. This Letter Agreement shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall not affect the validity or enforceability of this Letter Agreement or of any other term or provision hereof. Furthermore, in lieu of any such invalid or unenforceable term or provision, the parties hereto intend that there shall be added as a part of this Letter Agreement a provision as similar in terms to such invalid or unenforceable provision as may be possible and be valid and enforceable.

17.Governing Law. This Letter Agreement shall be governed by and construed and enforced in accordance with the laws of the State of New York, without giving effect to conflicts of law principles that would result in the application of the substantive laws of another jurisdiction. The parties hereto (i) all agree that any action, proceeding, claim or dispute arising out of, or relating in any way to, this Letter Agreement shall be brought and enforced in the courts of the State of New York located in the City and County of New York, Borough of Manhattan, and irrevocably submit to such jurisdiction and venue, which jurisdiction and venue shall be exclusive, and (i) waive any objection to such exclusive jurisdiction and venue or that such courts represent an inconvenient forum.

18.Notices. Any notice, consent or request to be given in connection with any of the terms or provisions of this Letter Agreement shall be in writing and shall be sent by express mail or similar private courier service, by certified mail (return receipt requested), by hand delivery or facsimile transmission.

[Signature Page Follows]

Sincerely,

PERIDOT ACQUISITION SPONSOR III, LLC

By:

Name: Jeffrey Gilbert

Title: General Counsel and Corporate Secretary

Tomas Ackerman

Preston Powell

Stephen Wedemeyer

Alan Levande

Edgar R. Giesinger

Michele J. Everard

Cheryl Lipshutz

Acknowledged and Agreed:

PERIDOT ACQUISITION CORP. III

By:

Name: Stephen Wedemeyer

Title: Chief Financial Officer

[Signature Page to Letter Agreement]