Supplemental Prospectus (Form 424B5)

Filed Pursuant to Rule 424(b)(5) and 424(b)(8)

Registration No. 333-294908

SUPPLEMENT TO PROSPECTUS SUPPLEMENT DATED APRIL 7, 2026

(To Prospectus dated April 7, 2026)

EXPLANATORY NOTE

This supplement is being filed solely for the purposes of filing the Exhibit 107 filing fee exhibit with respect to the underwriters' over-allotment option as described in the prospectus supplement, dated April 7, 2026 (File No. 333-294908), filed by Tamboran Resources Corporation with the Securities and Exchange Commission relating to 2,956,602 shares of common stock, $0.001 par value per share (3,400,093 if the underwriters' over-allotment option is exercised in full). This filing does not amend, modify or alter such prior filing in any other respect. No changes have been made to the prospectus supplement or the accompanying prospectus.