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

Any 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 and consent of the governing body. Any qualified elector appointed to fill a vacancy on the governing body shall serve until the next regular local election, at which time a qualified elector shall be elected to fill the remaining unexpired term, if any.