I like the question.
Ernest Hemingway’s novel The Sun Also Rises may be a little on the short side, compared at least to the standard Victorian novel against which many modernist writers positioned themselves, but it’s certainly long and complex enough to make more than just one statement about women or gender through the character of Brett Ashley. Allow me to suggest a couple of statements that the novel might be making, through Brett about women and gender.
1. Gender is in a state of change or redefinition. With her hat, her body (“built like the hull of a racing yacht,” the narrator Jake Barnes tells us), her sexual openness, and her circle of gay friends, Brett may be seen as a symbol of the “New Woman” or “flapper,” or more generally, she may be seen as a sign of the gradual changes in our cultural definitions of what it means to be a modern woman.
1. Women are a disruptive influence among men. The male characters’ shared desire for Brett is often central to the storyline, and that shared desire often ends in bad feelings and sometimes even fistfights among the men. By contrast, when Brett is absent (e.g. in Chapter XII, Jake and Bill’s Spanish fishing trip), Jake is at his most peaceful and feels reborn.
The enotes study guide (see the link below) may offer some other leads for you.