N.M. Stat. § 3-16-8
Unless otherwise provided for in the combined municipal organization charter, justices of the peace [magistrates] who have been elected and are holding office within the boundaries of the combined municipal organization at the time such government becomes operative, shall continue to hold office as justices of the peace [magistrates] for such combined municipal organization within their respective precincts for the term for which they have been elected, and their successors shall be elected at the time and in the manner and for the term provided by law for justices of the peace [magistrates]. Vacancies in office shall be filled by the governing body of the combined municipal organization for the term as provided for justices of the peace [magistrates] appointed to fill vacancies. Justices of the peace [magistrates] in the combined municipal organization shall exercise the same powers and jurisdiction as is provided by law for justices of the peace [magistrates].
NMS § 3-16-8