We saw in the trailer that Brienne and Podrick eventually meet up with Jaime and tells him that should she not convince the Blackfish to surrender, she may have to fight Jaime as she's pledged to the Starks. In the books, Brienne eventually finds Catelyn (which I believe will happen during the meeting with Blackfish), who believes Jaime to be responsible for the Red Wedding and sees Brienne carrying the sword he gave her, which causes Catelyn to think she's a traitor. In order to prove her loyalty, Catelyn demands she kill Jaime, which is what I think they're hinting at in the preview