So far as broadcast TV stories are concerned, we don't know. In other media, we've been given contradictory accounts:
In "Set Piece" (Virgin New Adventures novel), she left the Doctor to become Time's Vigilante, using a short-range time hopper mounted on a motorcycle to patrol a particular segment of time; in effect doing what the Doctor does, but on a smaller scale.
According to "Unit:Dominion" (audio story) & "The Lights of Skaro" (audio story) from Big Finish, she went to Gallifrey to study at the Academy, with the Doctor expecting her to become either a renegade Time Lord or Lord President of the High Council. (He, of course, managed to be both.)