Trevi Therapeutics, Inc.

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a) of the

Securities Exchange Act of 1934

(Amendment No. )

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195 Church Street, 16 th Floor

NOTICE OF 2026 ANNUAL MEETING OF STOCKHOLDERS

To be held June 3, 2026

You are cordially invited to attend the 2026 Annual Meeting of Stockholders of Trevi Therapeutics, Inc. The Annual Meeting is scheduled to be held exclusively online via the Internet as a virtual web conference at www.virtualshareholdermeeting.com/TRVI2026 on Wednesday, June 3, 2026 at 11:00 a.m. Eastern Time.

Only stockholders who owned common stock at the close of business on April 6, 2026, the record date for the Annual Meeting, can vote at the Annual Meeting or any adjournment or postponement that may take place. At the Annual Meeting, the stockholders will consider and vote on the following matters:

Election of one Class I director to our Board of Directors to serve until the 2029 Annual Meeting of Stockholders;

Ratification of the appointment of Ernst & Young LLP as our independent registered public accounting firm for the fiscal year ending December 31, 2026;

Approval, on an advisory basis, of the compensation paid to our named executive officers;

Approval of the Trevi Therapeutics, Inc. Amended and Restated 2019 Stock Incentive Plan;

Approval of an amendment to our Restated Certificate of Incorporation, as amended, to increase the number of authorized shares of common stock from 200,000,000 shares to 400,000,000 shares; and

Transaction of any other business properly brought before the Annual Meeting or any adjournment or postponement of the Annual Meeting.

A complete list of registered stockholders as of the close of business on April 6, 2026, the record date for the Annual Meeting, will be available for examination by any stockholder for any purpose germane to the Annual Meeting for a period of ten days ending on the day before the Annual Meeting at www.virtualshareholdermeeting.com/TRVI2026.

As noted above, our Annual Meeting will be a “virtual meeting” of stockholders, which will be conducted exclusively via the Internet. There will not be a physical meeting location and stockholders will not be able to attend the Annual Meeting in person. However, you may attend the Annual Meeting online, vote your shares electronically during the meeting and submit questions during the meeting by visiting www.virtualshareholdermeeting.com/TRVI2026.

In order to attend the Annual Meeting online, vote your shares and submit your questions electronically during the Annual Meeting, you must visit www.virtualshareholdermeeting.com/TRVI2026 on June 3, 2026 at 11:00 a.m. Eastern Time. Further information about how to attend the Annual Meeting online, vote your shares and submit questions is included in the accompanying proxy statement. As outlined in the accompanying proxy statement, the Board of Directors recommends that you vote in favor of the director nominee in proposal one, and in favor of proposals two, three, four and five.

You can find more information, including the nominee for director, in the accompanying proxy statement for the Annual Meeting, which is also available for viewing, printing and downloading at www.proxyvote.com.

Instead of mailing to our stockholders a printed copy of our proxy materials, including the accompanying proxy statement, the proxy card and our annual report to stockholders for the fiscal year ended December 31, 2025, we provide access to these materials via the Internet. This reduces the amount of paper necessary to produce these materials as well as the costs associated with mailing these materials to all stockholders. Accordingly, on or about April 23, 2026, we plan to mail a Notice of Internet Availability of Proxy Materials, or Notice, to all stockholders of record at the close of business on April 6, 2026, the record date for the Annual Meeting, and we will post our proxy materials on the website referenced in the Notice. As more fully described in the Notice, stockholders may choose to access our proxy materials on the website referred to in the Notice or may request to receive a printed or e-mailed set of our proxy materials. In addition, the Notice and website provide information regarding how you may request to receive proxy materials in printed form by mail, or electronically by email, on an ongoing basis.

If you are a stockholder of record, you may vote or submit a proxy to vote in one of the following ways:

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Submit a Proxy to Vote Over the Internet Prior to the Annual Meeting, by going to www.proxyvote.com to complete an electronic proxy card (have your notice or proxy card in hand when you visit the website) or scanning the QR code on the proxy card with your smartphone. You will be asked to provide the control number from your proxy card. Internet voting is available 24 hours a day, 7 days a week, until 11:59 p.m., Eastern Time, on June 2, 2026;

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Submit a Proxy to Vote Over the Telephone, by calling 1-800-690-6903 and following the instructions. Have your proxy card available when you call. You will be asked to provide the control number from your proxy card. Telephone voting is available 24 hours a day, 7 days a week, until 11:59 p.m., Eastern Time, on June 2, 2026;

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Submit a Proxy to Vote Through the Mail, if you received (or requested and received) a printed copy of the proxy materials, by completing, signing and dating the proxy card that accompanies this proxy statement and returning it promptly in the postage-prepaid envelope provided or return it to Vote Processing, c/o Broadridge, 51 Mercedes Way, Edgewood, NY 11717. Your completed, signed and dated proxy card must be received by 11:59 p.m., Eastern Time, on June 2, 2026; or

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Vote Over the Internet During the Annual Meeting, while virtually attending the Annual Meeting by visiting www.virtualshareholdermeeting.com/TRVI2026. Have your notice or proxy card in hand when you visit the Annual Meeting website and follow the instructions.

If your shares are held in “street name,” that is, held for your account by a bank, broker or other nominee, you will receive instructions from the bank, broker or other nominee that you must follow for your shares to be voted.

Whether or not you plan to attend the Annual Meeting, we urge you to take the time to submit your proxy to vote your shares.

By order of the Board of Directors,

Jennifer L. GoodPresident and Chief Executive OfficerNew Haven, ConnecticutApril 21, 2026

Trevi Therapeutics, Inc.

Proxy Statement