New Mexico Statutes Chapter 3. Municipalities § 3-12-1. Vacancy on governing body;  appointment;  procedures

A. A vacancy on the governing body of a mayor-council municipality shall be filled by appointment of a qualified elector by the mayor of the municipality, with the advice, the consent and a majority vote of the members of the governing body that are present;  provided that the governing body shall vote at the next meeting immediately following the vacancy to fill the vacancy if the vacancy has not been filled within fifteen days after the vacancy occurred;  and provided further that so long as the vacancy remains unfilled, the item shall be included on each subsequent governing body meeting agenda until the vacancy is filled.

B. A qualified elector appointed to fill a vacancy on the governing body shall serve until the next regular local election or municipal officer election, whichever is applicable, at which time a qualified elector shall be elected to fill the remaining unexpired term, if any.