Fem!Harry is very angry at the world. She's been angry as far as she can remember and her treatment at the Dursley's only made it worse. She is resentful of "normal" people because she feels they don't know suffering, and sees that often times there are people that seem horrible that have all kinds of things that she doesn't, even though she has done her best to "earn" them. This carries over to hogwarts where she is abrasive and has no real friends, except for maybe the quidditch team. Despite her anger she can't help but help people, and so years 1 and 2 have roughly the same end results. In year 3, however, she has no time turner (because she has no Hermione) and Sirius gets kissed in front of her. Fem!Harry thought she knew loss but she's never had anything to lose, and now as soon as she gets it she has it ripped away. Then she gets sent back to the Dursleys.
Enter Harry.
Fem!Harry is at her lowest point when Harry arrives. He's come from another world (I'm thinking through Deathly Hallows/Afterlife Train Station fuckery) and resolves to help Fem!Harry. Fem!Harry feels a connection to Harry right away, but it wary of getting close to people. Harry isn't a kid in this story. He's an old man, he's got silver hair streaked through with dark grey, he's got wrinkles around his eyes, and he's lived a full life in his own world before coming to this new one. Harry is like Uncle Iroh from Atla, while Fem!Harry is like Zuko from Atla. Harry guides and mentors her through challenges and trials, and she learns from him.
This is very much a premise with no extended plans. Could be a lesbian Flowerpot, could be another pairing, could be no pairing at all. Just that the mentor relationship needs to be there between Old-Man-Harry and Angry-Fem!Harry.