What happens if my ex-husband drives for a taxi cab, got in an accident, settled out of court but other party sued in another state?

Settled as a plaintiff or as a defendant?

I do not understand your question. If he settled the case, the case is settled and the other party can no longer maintain a civil suit in any state.

Who cares? I am not licensed in that State and he's your X.

If the settlement was done properly with a full and final release obtained in exchange for payment, then he can bring a motion to have the out of state lawsuit dismissed as moot. If he did something funky and didn't get a full and final release, he's screwed, the "settlement" is not binding, and he's got to defend the other case. He may still have a defense for the monies paid. He needs to be discussing this with his employer as well.