Star Wars has a tradition of two villains per movie:
1) Tarkin/Vader
2) Vader/Fett
3) Emperor/Vader
My idea is a Godfather-like crime boss whose organization fled to the Outer Rim under the harsh rule of the Empire, but now seeks to undermine the fledgling new Republic. His son is strong in the Force and has learned the ways of the dark side from ancient Sith artifacts and seeks to supplant his father.