An independent candidacy? Against an incumbent POTUS and a Dem challenger? I doubt it.
I think it's more likely she runs for her own former Senate seat in NY, and settles for a Kennedy-esque "lion of the Senate" role in history.
Gillibrand isn’t going to roll over and play dead for her.
Schumer isn’t either.
She needs to find a new state with a Democrat senate vacancy.
I hear she was always a fan of the Twins...