Fellow’s finished? Not quite finished (3)
I believe the answer is:
don
'fellow's' is the definition.
(both can mean an academic)
'finished? not quite finished' is the wordplay.
'finished?' becomes 'done' (both can mean completed).
'not quite finished' means to remove the last letter (most but not all of the word).
'done' with its final letter taken off is 'DON'.
(Other definitions for don that I've seen before include "Spanish nobleman" , "and 13 Down: Mozart opera" , "Spaniard in a University?" , "Put on; man's name" , "Put on; college teacher" .)