Brienne has never been afraid to stand up for justice, even when it puts her in the eye of danger. She proves this when she stands up for Jaime during his trial after he arrives in Winterfell. Jaime is up against the heads of two households he has irredeemably wrecked: Daenerys Targaryen and Sansa Stark. Daenerys tells Jaime that she used to talk with her late brother about what they would do to the former Kingsguard when they reclaimed the throne, but her issue with him is kind of moot since no one else has a problem with the death of the Mad King. Sansa initially agrees with Daenerys, since Jaime was directly involved with the capture of her father before he was killed by Jaime's son, Joffrey. Enter Brienne.
She cannot stand by as Jaime is raked over the coals for his past, standing up to ask that the two other women trust Jaime. "He is a man of honour," she swears before Sansa, Dany, and Jon (who looks like he'd rather be anywhere else, honestly), telling the Lady of Winterfell specifically that without Jaime, she would have never been able to protect Sansa when the time came. Brienne reveals to Sansa that both she and Jaime swore an oath to her mother, Catelyn Stark, that they would bring her daughters back home to Winterfell. It's only after Brienne assures Sansa that she trusts Jaime with her life that the younger woman backs down.
Not only is this a boss moment for Brienne, standing up for the Dragon Queen and the woman she pledged her sword to, it's also a touching moment that sheds light on how deeply Sansa trusts Brienne. As the Lady of Winterfell later tells Dany, she trusts Brienne with her own life and that means a lot coming from a woman with Sansa's past. Brienne isn't just a loyal friend, she inspires the same sort of loyalty from those around her, which is the mark of a truly good woman.