Exhibit (a)(1)(i)

Cover Letter to Offer to Purchase and Letter of Transmittal

Princeton Everest Fund

June 20, 2025

Dear Princeton Everest Fund Shareholder:

Princeton Everest Fund (the “Fund”) is a closed-end fund which offers shares that do not have daily liquidity. To provide Fund shareholders (“Shareholders”) with periodic liquidity, the Fund offers a share repurchase program which enables Shareholders to sell shares at Net Asset Value (“NAV”) on a specific repurchase date. We have outlined important dates below related to the tender offer by the Fund.

If you are not interested in selling your shares of beneficial interest of the Fund (the “Shares”) at this time, please disregard this notice and take no action.

The tender offer period will begin on June 20, 2025 and end on July 18, 2025 (unless the offer is extended), and any Shares tendered to the Fund will be valued with effect on September 30, 2025 for purposes of calculating the purchase price of such Shares. The purpose of the tender offer is to provide liquidity to Shareholders. Shares can be redeemed by means of a tender offer only during one of the Fund’s announced tender offers. There can be no assurance that the Fund will be able to repurchase all the Shares that you tender even if you tender all the Shares that you own.

Should you wish to sell any of your Shares during this tender offer period and you hold your Shares directly, please complete and return the enclosed Letter of Transmittal to the Fund’s transfer agent, Ultimus Fund Solutions, LLC (“UFS”) by mail. If you would like the Fund to purchase your Shares and a custodian holds your Shares on your behalf, please complete and send the Letter of Transmittal to your custodian and direct your custodian to execute it and mail it to UFS.

All requests to tender Shares must be received in good order by UFS, whether sent directly or through your custodian, by July 18, 2025, unless the offer is extended. If you elect to tender, please confirm receipt of the Letter of Transmittal by UFS by calling the Fund at 855.924.2454 or working with your custodian to contact UFS. Please allow 48 hours for your Letter of Transmittal to be processed prior to contacting UFS, whether sent directly or through your custodian, to confirm receipt. If you fail to confirm receipt of your Letter of Transmittal by UFS, there can be no assurance that your tender has been received by the Fund.

If you have any questions, please refer to the attached Offer to Purchase document, which contains additional important information about the tender offer, or call the Fund at 855.924.2454.

Sincerely,

Princeton Everest Fund