While Jaime and Brienne are taking their bath at Harrenhal, and he’s sharing the story of how he became the Kingslayer, he asks himself:
I’d say Brienne’s age is in the 18-20 range when we meet her in A Clash of Kings. She’s past the age of majority, but she is hilariously, adorably naive. Which explains a lot about her going off to serve King Renly! Jaime’s in his 30s, and suffering no lack of cynicism.
And, indeed, Jaime: why ARE you sharing your story with this “ugly absurd child” when you haven’t even told your own siblings?
The Monster's Ink 
Brienne was SUCH a redemptive factor for Jaime in his storyline. Thank goodness he finally had someone to talk to about stuff that he wasn’t going to tell anyone else.
She will continue to be a redemptive factor in Jaime’s storyline.