Exhibit 1.2

[Letterhead of Sandler O’Neill & Partners, L.P.]

August 17, 2016

Mr. Joseph D. Roberto

Chairman, President and Chief Executive Officer

PCSB Bank

2651 Strang Boulevard

Suite 100

Yorktown Heights, NY 10598

Dear Mr. Roberto:

We understand that the Board of Trustees of PCSB Bank (the “Bank”) is considering the adoption of a Plan of Conversion (the “Plan”) pursuant to which the Bank will be converted into stock form and shares of the common stock (the “Common Stock”) of a newly organized stock holding company (the “Holding Company”) for the Bank will be offered and sold to the Bank’s eligible depositors and certain tax-qualified employee benefit plans in a subscription offering and, to the extent shares remain available, to members of the Bank’s community in a community offering and, under certain circumstances, to the general public in a syndicated community offering or a firm commitment public offering (collectively, the “Offering”). The Holding Company and the Bank are sometimes collectively referred to herein as the “Company.” Sandler O’Neill & Partners, L.P. (“Sandler O’Neill”) is pleased to act as records management agent (“Records Agent”) for the Bank in connection with the Offering. This letter is to confirm the terms and conditions of our engagement.

SERVICES AND FEES

In our role as Records Agent, we anticipate that our services will include the services outlined below, each as may be necessary and as the Company may reasonably request:

Each of these services is further described in Appendix A to this agreement.

For its services hereunder, the Company agrees to pay Sandler O’Neill a fee of $30,000. This fee is based upon the requirements of current regulations and the Plan as currently contemplated. Any unusual or additional items or duplication of service required as a result of a material change in the regulations or the Plan as currently contemplated or a material delay or other similar events may result in extra charges that will be covered in a separate agreement if and when they occur, but in no event shall such additional fees exceed $20,000. All fees under this agreement shall be payable in cash, as follows: (a) $10,000 payable upon execution of this agreement, which shall be non-refundable; and (b) the balance upon the mailing of proxy and offering materials to the Bank’s eligible account holders.

COSTS AND EXPENSES

In addition to any fees that may be payable to Sandler O’Neill hereunder, the Company agrees to reimburse Sandler O’Neill, upon request made from time to time, for its reasonable out-of-pocket expenses incurred in connection with its engagement hereunder, regardless of whether the Offering is consummated, including, without limitation, travel, lodging, meals, telephone, postage and other similar expenses, up to a maximum of $25,000. It is understood that all expenses associated with the operation of the Conversion Center will be borne by the Company. The provisions of this paragraph are not intended to apply to or in any way impair the indemnification provisions of this agreement.

RELIANCE ON INFORMATION PROVIDED

The Company will furnish Sandler O’Neill with such information as Sandler O’Neill reasonably believes appropriate to its assignment (all such information so furnished being the “Records”). The Company recognizes and confirms that Sandler O’Neill (a) will use and rely primarily on the Records without having independently verified the same, and (b) does not assume responsibility for the accuracy or completeness of the Records. The Company will also inform Sandler O’Neill within a reasonable period of time of any changes in the Plan that require changes in Sandler O’Neill’s services.

CONFIDENTIALITY

Except as contemplated in connection with the performance of its services under this agreement, as authorized by the Company or as required by law, regulation or legal process, Sandler O’Neill agrees that it will treat as confidential all material, non-public information relating to the Company obtained in connection with its engagement hereunder (the “Confidential Information”); provided, however, that Sandler O’Neill may disclose such information to its agents and advisors who are assisting or advising Sandler O’Neill in performing its services hereunder and who have been directed to comply with the terms and conditions of this paragraph. As used in this paragraph, the term “Confidential Information” shall not include information which (a) is or becomes generally available to the public other than as a result of a disclosure by Sandler O’Neill in breach of the confidentiality provisions contained herein, (b)

was available to Sandler O’Neill on a non-confidential basis prior to its disclosure to Sandler O’Neill by the Company, (c) becomes available to Sandler O’Neill on a non-confidential basis from a person other than the Company who is not otherwise known to Sandler O’Neill to be bound not to disclose such information pursuant to a contractual, legal or fiduciary obligation owed to the Company, or (d) is independently developed by Sandler O’Neill without use of or reference to the Confidential Information disclosed hereunder.

LIMITATIONS

Sandler O’Neill, as Records Agent, (a) shall have no duties or obligations other than those specifically set forth herein; (b) will be regarded as making no representations and having no responsibilities as to the validity, sufficiency, value or genuineness of any order form or any stock certificates or the shares represented thereby, and will not be required to and will make no representations as to the validity, value or genuineness of the offer; (c) shall not be liable to any person or entity, including the Company, by reason of any error of judgment or for any act done by it in good faith, or for any mistake of law or fact in connection with this agreement and the performance hereof unless caused by or arising out of its own willful misconduct, bad faith or gross negligence; (d) will not be obliged to take any legal action hereunder which might in its judgment involve any expense or liability, unless it shall have been furnished with reasonable indemnity satisfactory to it; and (e) may rely on and shall be protected in acting in reliance upon any certificate, instrument, opinion, notice, letter, telex, telegram, or other document or security delivered to it and in good faith believed by it to be genuine and to have been signed by the proper party or parties.

Anything in this agreement to the contrary notwithstanding, in no event shall Sandler O’Neill be liable for special, indirect or consequential loss or damage of any kind whatsoever (including but not limited to lost profits), even if Sandler O’Neill has been advised of the likelihood of such loss or damage and regardless of the form of action.

INDEMNIFICATION

The Company agrees to indemnify and hold Sandler O’Neill and its affiliates and their respective partners, directors, officers, employees, agents and controlling persons (Sandler O’Neill and each such person being an “Indemnified Party”) harmless from and against any and all losses, claims, damages and liabilities, joint or several, to which such Indemnified Party may become subject under applicable federal or state law, or otherwise, related to or arising out of the engagement of Sandler O’Neill pursuant to, and the performance by Sandler O’Neill of the services contemplated by, this letter, and will reimburse any Indemnified Party for all expenses (including reasonable counsel fees and expenses) as they are incurred, including expenses incurred in connection with the investigation of, preparation for or defense of any pending or threatened claim or any action or proceeding arising therefrom, whether or not such Indemnified Party is a party. The Company will not be liable under the foregoing indemnification provision to the extent that any loss, claim, damage, liability or expense is found in a final judgment by a court of competent jurisdiction to have resulted primarily from Sandler O’Neill’s willful misconduct, bad faith or gross negligence.

REPRESENTATIONS

The Company represents and warrants that it has all requisite power and authority to enter into and carry out the terms and provisions of this agreement, the execution, delivery and performance of this agreement does not breach or conflict with any agreement, document or instrument to which it is a party or bound and this agreement has been duly authorized, executed and delivered by the Company.

MISCELLANEOUS

The following addresses shall be sufficient for written notices to each other:

The agreement and appendix hereto constitute the entire agreement between the parties with respect to the subject matter hereof and can be altered only by written consent signed by the parties. This agreement is governed by the laws of the State of New York.

[signature page follows]

Please confirm that the foregoing correctly sets forth our agreement by signing and returning to Sandler O’Neill the duplicate copy of this letter enclosed herewith.

APPENDIX A

OUTLINE OF RECORDS AGENT SERVICES

A-1