If I remember correctly Carol was working at a scientific outpost that was attacked by Chang's prototype BoP. It was one of the reasons Kirk was so staunchly anti-Klingon in TUC.
I also wanted to note that in the Shatnerverse Kirk and Carol were spending retirement together in The Ashes of Eden
. He was suffering erectile dysfunction before Teilani used her wiles to lure him away to Chal.