The web site says that Regents requires a scholarship application (due Dec 1). Students apply here (requires a login, probably the same as their applicant portal): Scholarship Details
And here is the brief description:
The Regents Scholars Scholarship Program provides funding to cover average tuition and fees, room and board, and books to high-achieving freshman students who meet specific criteria. The award is renewable for four years if the student meets renewal criteria each year.
Regents Scholars will be involved in innovative and exciting programs and opportunities. To enhance the students’ academic experiences, each scholar will be assigned one of UNM’s outstanding faculty, who will serve as a mentor.
Regents Scholars will be admitted to the University of New Mexico Honors College and will receive specialized advisement and course registration privileges. They will also represent the University at various community and University functions.