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. )

Filed by the Registrant ☒ Filed by a Party other than the Registrant ☐

Check the appropriate box:

☐	Preliminary Proxy Statement
☐	Confidential, for Use of the Commission Only (as permitted by Rule 14a-6(e)(2))
☐	Definitive Proxy Statement
☒	Definitive Additional Materials
☐	Soliciting Material under §240.14a-12

TREVI THERAPEUTICS, INC.

(Name of Registrant as Specified In Its Charter)

(Name of Person(s) Filing Proxy Statement, if other than the Registrant)

Payment of Filing Fee (Check all boxes that apply):

☒	No fee required.
☐	Fee paid previously with preliminary materials.
☐	Fee computed on table in exhibit required by Item 25(b) per Exchange Act Rules 14a-6(i)(1) and 0-11.

P.O. BOX 8016, CARY, NC 27512-9903 Have your ballot ready and please use one of the methods below for easy voting: Your vote matters! Have the 12 digit control number located in the box above availablewhen you access the website and follow the instructions. Your control number Scan QR for digital voting Internet: Trevi Therapeutics, Inc. Annual Meeting of Stockholders www.proxypush.com/TRVI • Cast your vote online • Have your Proxy Card ready • Follow the simple instructions to record your vote For stockholders of record on April 15, 2024 Phone: 1-866-430-8292 Thursday, June 13, 2024 12:30 p.m., Eastern • Use any touch-tone telephone Time • Have your Proxy Card ready • Follow the simple recorded instructions Mail: • Mark, sign and date your Proxy Card • Fold and return your Proxy Card in the postage-paid YOUR VOTE IS IMPORTANT! envelope provided PLEASE VOTE BY: 12:30 p.m., Eastern Time, June 13, 2024. This proxy is being solicited on behalf of the Board of Directors The undersigned hereby appoints Jennifer Good, Lisa Delfini and Christopher Galletta (the "Named Proxies"), and each of them, as the true and lawful attorneys of the undersigned, with full power of substitution and revocation, and authorizes them, and each of them, to vote all the shares of capital stock of Trevi Therapeutics, Inc. which the undersigned is entitled to vote at said meeting and any adjournment or postponement thereof upon the matters specified and upon such other matters as may be properly brought before the meeting or any adjournment or postponement thereof, conferring authority upon such true and lawful attorneys to vote in their discretion on such other matters as may properly come before the meeting and revoking any proxy heretofore given. THE SHARES REPRESENTED BY THIS PROXY WILL BE VOTED AS DIRECTED OR, IF NO DIRECTION IS GIVEN, SHARES WILL BE VOTED IN ACCORDANCE WITH THE BOARD OF DIRECTORS' RECOMMENDATION. This proxy, when properly executed, will be voted in the manner directed herein. In their discretion, the Named Proxies are authorized to vote upon such other matters that may properly come before the meeting or any adjournment or postponement thereof. You are encouraged to specify your choice by marking the appropriate box (SEE REVERSE SIDE) but you need not mark any box if you wish to vote in accordance with the Board of Directors’ recommendation. The Named Proxies cannot vote your shares unless you sign (on the reverse side) and return this card. PLEASE BE SURE TO SIGN AND DATE THIS PROXY CARD AND MARK ON THE REVERSE SIDE Copyright © 2024 BetaNXT, Inc. or its affiliates. All Rights Reserved

Trevi Therapeutics, Inc. Annual Meeting of Stockholders Please make your marks like this: THE BOARD OF DIRECTORS RECOMMENDS A VOTE: FOR THE DIRECTOR NOMINEES AND FOR PROPOSAL 2 BOARD OF DIRECTORS PROPOSALS YOUR VOTE RECOMMENDS 1. Election of three Class II directors to our Board of Directors, each to serve until the 2027 Annual Meeting of Stockholders: FOR WITHHOLD 1.01 Dominick Colangelo FOR #P2# #P2# 1.02 Edward Mathers FOR #P3# #P3# 1.03 David Meeker, M.D. FOR #P4# #P4# FOR AGAINST ABSTAIN 2. Ratification of the appointment of Ernst & Young LLP as our independent registered public FOR #P5# #P5# #P5# accounting firm for the fiscal year ending December 31, 2024. NOTE: Transaction of any other business properly brought before the Annual Meeting or any adjournment or postponement of the Annual Meeting. You must register prior to the deadline of June 12, 2024 at 5:00 p.m. Eastern Time to attend the meeting online and/or participate at www.proxydocs.com/TRVI. Authorized Signatures - Must be completed for your instructions to be executed. Please sign exactly as your name(s) appears on your account. If held in joint tenancy, all persons should sign. Trustees, administrators, etc., should include title and authority. Corporations should provide full name of corporation and title of authorized officer signing the Proxy Card. Signature (and Title if applicable) Signature (if held jointly)