The Arkansas Supreme Court is currently selected in non-partisan elections. "The Arkansas Bar Association is holding a series of public forums across the state to discuss and
receive comments on a proposed Arkansas Constitutional Amendment on an appointment process
for selection of Supreme Court Justices," according to a press release by the Bar Association.
The proposal recommends “a nine-member judicial nominating commission...be formed to accept applications, interview candidates and nominate three for each vacancy on the Supreme Court.”, according to the Brennan Center, which goes on to say: the governor “would then appoint one of those candidates to the court” for a single, non-renewable, 14-year term.
FWIW, I like the single, non-renewable, 14-year term as that helps judicial independence without going to the extreme of allowing a justice to remain on the state's high court for 20 or 30 years.