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.