The story might progress as Harry, in his new female form, forms new alliances with female characters. They could band together to fight against some sort of misogynistic force in the wizarding world. He could also have a different kind of friendship with Hermione now, as they share more of a sisterly bond. And his relationship with Ron could become more complex, with Ron perhaps having some unexpected feelings for Harry in his new form.
One way the story could progress is that Harry, now as a girl, could infiltrate female - only areas in the wizarding world. This could lead to uncovering secrets that were previously hidden from male characters. He might also have to deal with unwanted attention from some male characters, which would add a new layer of conflict to the story.