Gov. Susana Martinez, whose appointee to the Court of Appeals lost his seat in Tuesday's election, will get another shot at putting a Republican on the bench.
Court of Appeals Judge Celia Foy Castillo is retiring in December.
A bipartisan commission will consider applications for the position and then forward a list of candidates to the governor.
Judges then run in a partisan election if they want to keep their job. If they win, they face periodic nonpartisan retention elections.
Martinez has made numerous appointments to the state's courts since taking office. However, only two of her nine appointees running in contested races on Tuesday kept their seats.
Democrat Monica Zamora, a district judge in Albuquerque, defeated Court of Appeals Judge Miles Hanisee. Martinez's Supreme Court appointee, Justice Paul Kennedy, lost to District Judge Barbara Vigil of Santa Fe.