NO...
If you kill the Apprentice, then Uthar tells you that your "destiny has something else in store for you". Thats all that you can do at the academy then.
HOWEVER...
You could take the Double-Double Cross misson. In this quest, you get to kill the Apprentice Lady and Uthar. With the apprentice and the master dead, you technically are the new master of the academy. But -
It's a very dark sided action and it will empty the academy, but it's better than just doing nothing.