Company: HYAC-WT
Filing Date: 2025-07-15
Form Type: DEFA14A
Source: 0001104659-25-068092
Chunk: 0

Company: Haymaker Acquisition Corp. 4
Filing Date: 2025-07-15
Form: DEFA14A
Chunk 0
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<div align='center'>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. )</div>

Filed by the Registrant x

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                                                      |
| x | Definitive Additional Materials                                                 |
| ¨ | Soliciting Material under §240.14a-12                                           |

<div align='center'>HAYMAKER ACQUISITION CORP. 4

(Name of Registrant as Specified In Its Charter)

(Name of Person(s) Filing Proxy Statement, if other than the Registrant)</div>

Payment of Filing Fee (Check the appropriate
box):

| x | No fee required.                                                              |
| ¨ | Fee paid previously with preliminary materials.                               |
| ¨ | Fee computed on table in exhibit per Exchange Act Rules 14a-6(i)(1) and 0-11. |

<div align='center'>SUPPLEMENT TO DEFINITIVE PROXY STATEMENT

FOR THE ANNUAL GENERAL MEETING OF SHAREHOLDERS OF
HAYMAKER ACQUISITION CORP. 4
TO BE HELD ON JULY 24, 2025</div>

On July 1, 2025, Haymaker Acquisition Corp. 4 (the “Company”)
filed with the Securities and Exchange Commission a definitive proxy statement on Schedule 14A (the “Proxy Statement”)
relating to the Company’s annual general meeting of shareholders to be held on July 24, 2025 at 10:00 a.m., Eastern Time (the “Annual Meeting”).

The Company is providing this proxy statement supplement (this “Supplement”)
solely to (i) correct the per-share price at which public shares will be redeemed for a pro rata portion of the funds held in the trust
account established in connection with our IPO (the “Trust Agreement”) at the time of the Annual Meeting (the “Redemption Price”) in the Proxy Statement to $11.05, which was previously stated as $10.