Bran will come to Jaime’s aid
The last time Bran and Jaime crossed paths, the Kingslayer pushed Bran out an open window. But hear me out. Over the course of seven seasons, Bran has left behind the innocent, tower-climbing boy he once was and has evolved into the Three-Eyed Raven, someone who seems very unconcerned with human drives like revenge. As he’s said himself, he’s not really Bran anymore, so to speak.
Jaime and Bran reunited at the end of the premiere episode, “Winterfell.” Jaime looked shook, but I don’t think he needs to worry about Bran telling his secret. He does need to worry about Daenerys Targaryen being angry with him for killing her father, and about a lot of Northerners who are none too keen on the Lannisters. But that’s another story.
I believe that Bran will come to Jaime’s defense because he knows how crucial the Kingslayer will be in the coming war. He doesn’t care about being pushed out of a tower anymore, because that incident led him down the path he’s on now. I think Bran will surprise us by advocating for Jaime’s life, perhaps backing up Tyrion and Brienne when and if they explain the extenuating circumstances surrounding the murder of King Aerys.