New mexico constitution
Article XX: miscellaneous
Section 5

If, while the senate is not in session, a vacancy occur in any office the incumbent of which was appointed by the governor by and with the advice and consent of the senate, the governor shall appoint some qualified person to fill the same until the next session of the senate; and shall then appoint by and with the advice and consent of the senate some qualified person to fill said office for the period of the unexpired term.