In New Mexico, judges who are appointed to fill a vacancy must run to keep their seats in the next general election. These judicial races are partisan ones. If you are appointed and don’t win, you will be back in private practice (just like me).
Thus, Justice Shannon Bacon and Justice David Thomson, who were appointed to the Supreme Court by Governor Lujan Grisham earlier this year, must run in the November 2020 general election.
Their first campaign event (as far as I’m aware) will be next Thursday evening in Santa Fe at the law firm of Brian Egolf, Speaker of the New Mexico House of Representatives.
Justice Bacon and Justice Thomson have also set up their campaign websites here and here. Their websites make clear that each of them will be seeking public financing for their elections.
I do not know of anyone who has declared an intent to run against them, but there’s still plenty of time for that. It’s possible that they could face primary challenges from fellow Democrats, or a challenge in the general election from Republicans or Libertarians, or both. But when I do hear news, I’ll post it here.