Exhibit 5.4

6 August 2020

Matter No.: 360032

Tel: 441 279 5327

Email: jacqueline.king@conyers.com

Iterum Therapeutics Bermuda Limited

Clarendon House

2 Church Street

Hamilton HM 11

Bermuda

Dear Sirs

Re: Iterum Therapeutics Bermuda Limited (the “Company”)

We have acted as special Bermuda legal counsel to the Company in connection with a registration statement on Form S-1 (Registration No. 333-237326) originally filed with the U.S. Securities and Exchange Commission (the “Commission”) on 20 March 2020 (the “Registration Statement”, which term includes any amendments thereto but does not include any other document or agreement whether or not specifically referred to therein or attached as an exhibit or schedule thereto) relating to the registration under the U.S. Securities Act of 1933, as amended, (the “Securities Act”) of 8,400 units, each consisting of a $1,000 principal amount 6.500% exchangeable senior subordinated note due 2025 (the “Notes”) and 50 limited recourse royalty-linked subordinated notes (the “RLNs” and together with the Notes and the units, the “Securities”), each to be issued by the Company.

For the purposes of giving this opinion, we have examined the following documents:

The documents listed in items (ii) and (iii) above are herein sometimes collectively referred to as the “Documents” (which term does not include any other document or agreement whether or not specifically referred to therein or attached as an exhibit or schedule thereto).

We have also reviewed the memorandum of association and the bye-laws of the Company (together, the “Constitutional Documents”), each certified by the Secretary of the Company on 6 August 2020, minutes of the meetings of its directors held on 14 January 2020 and 6 August 2020 and the resolutions adopted by the Finance Committee of Iterum Therapeutics plc on 15 January 2020, 20 March 2020, 13 July 2020 and 5 August 2020 (together the “Resolutions”), and the notice to the public issued by the Bermuda Monetary Authority dated 1 June 2005 (the “Consent”). We have also reviewed such other documents and made such enquiries as to questions of law as we have deemed necessary in order to render the opinion set forth below.

We have assumed (a) the genuineness and authenticity of all signatures and the conformity to the originals of all copies (whether or not certified) examined by us and the authenticity and completeness of the originals from which such copies were taken; (b) that where a document has been examined by us in draft form, it will be or has been executed in the form of that draft, and where a number of drafts of a document have been examined by us all changes thereto have been marked or otherwise drawn to our attention; (c) the capacity, power and authority of all parties other than the Company to enter into and perform their obligations under any and all documents entered into by such parties in connection with the issuance of the Securities, and the due execution and delivery thereof by each party thereto, other than the Company; (d) the due execution and delivery of the Documents by each of the parties thereto, other than the Company, and the physical delivery thereof by the Company with an intention to be bound thereby; (e) that the Company will issue the Securities in furtherance of its objects as set out in its memorandum of association, (f) that the Constitutional Documents will not be amended in any manner that would affect the opinions expressed herein, (g) that upon the issuance of the Securities, the Bermuda Monetary Authority will not have revoked or amended its Consent; (h) that the Company will comply, to the extent applicable, with the requirements of Part III of the Companies Act 1981 of Bermuda entitled “Prospectuses and Public Offers”, (i) the accuracy and completeness of all factual representations made in the Registration Statement and other documents reviewed by us; (j) that the Resolutions were passed at one or more duly convened, constituted and quorate meetings or by unanimous written resolutions, remain in full force and effect and have not been rescinded or amended; (k) that there is no provision of the law of any jurisdiction, other than Bermuda, which would have any implication in relation to the opinions expressed herein; (l) the validity and binding effect under the laws of the State of New York (the “Foreign Laws”) of the Documents in accordance with their respective terms; (m) the validity and binding effect under the Foreign Laws of the submission by the Company pursuant to the Documents to the jurisdiction of the courts of the State of New York or the courts of the United States located in the Borough of Manhattan, New York City, New York; (n) that none of the parties to the Documents carries on business from premises in Bermuda at which it employs staff and

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pays salaries and other expenses; (o) that the issuance and sale of and payment for the Securities will be in accordance with the Registration Statement (including the prospectus set forth therein and any applicable supplement thereto); and (p) that on the date of entering into the Documents the Company is and after entering into the Documents will be able to pay its liabilities as they become due.

The obligations of the Company in connection with any Security or other agreement or document relating thereto, including the Documents, (a) will be subject to the laws from time to time in effect relating to bankruptcy, insolvency, liquidation, possessory liens, rights of set off, reorganisation, amalgamation, merger, moratorium or any other laws or legal procedures, whether of a similar nature or otherwise, generally affecting the rights of creditors as well as applicable international sanctions; (b) will be subject to statutory limitation of the time within which proceedings may be brought; (c) will be subject to general principles of equity and, as such, specific performance and injunctive relief, being equitable remedies, may not be available; (d) may not be given effect to by a Bermuda court, whether or not it was applying the Foreign Laws, if and to the extent they constitute the payment of an amount which is in the nature of a penalty; and (e) may not be given effect by a Bermuda court to the extent that they are to be performed in a jurisdiction outside Bermuda and such performance would be illegal under the laws of that jurisdiction. Notwithstanding any contractual submission to the jurisdiction of specific courts, a Bermuda court has inherent discretion to stay or allow proceedings in the Bermuda courts.

We express no opinion as to the enforceability of any provision of the Documents which provides for the payment of a specified rate of interest on the amount of a judgment after the date of judgment or which purports to fetter the statutory powers of the Company.

We have made no investigation of and express no opinion in relation to the laws of any jurisdiction other than Bermuda. This opinion is to be governed by and construed in accordance with the laws of Bermuda and is limited to and is given on the basis of the current law and practice in Bermuda. This opinion is issued solely for the purposes of the filing of the Registration Statement and the issuance of the Securities by the Company as described in the Registration Statement and is not to be relied upon in respect of any other matter.

On the basis of and subject to the foregoing, we are of the opinion that:

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We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the references to our firm under the caption “Legal Matters” in the prospectus forming a part of the Registration Statement. In giving such consent, we do not hereby admit that we are experts within the meaning of Section 11 of the Securities Act or that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations of the Commission promulgated thereunder.

Yours faithfully,

/s/ Conyers Dill & Pearman Limited

Conyers Dill & Pearman Limited

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