N.M. Stat. § 22-5-8
Term of office.
A. The full term of office of a member of a local school board shall be four years
succeeding the member's election to office at a regular local election held pursuant to
the Local Election Act [Chapter 1, Article 22 NMSA 1978].
B. Any member of a local school board whose term of office has expired shall
continue in that office until a successor is elected and qualified.