I feel bad for Capt. Klaa. He went from commanding his own ship to being a translator? That can't be a promotion in the Klingon Empire.
It was probably part of Klaa's punishment for screwing up in ST V.
I always thought that Klaa volenteered to serve as Kirk's translator. He knew Kirk as a man of honor, and they had earned each others respect by the end of the Sha Ka Re informal "conference".