Finished first, say, at university, having an advantage (3,2)
I believe the answer is:
one up
'having an advantage' is the definition.
(I've seen this before)
'finished first say at university' is the wordplay.
'finished first' becomes 'won' (I've seen this in another clue).
'say' shows a homophone (sound like).
'at university' becomes 'up' (slang term meaning at university).
'won' is a homophone of 'one'.
'one'+'up'='ONE-UP'
(Other definitions for one up that I've seen before include "Horse rider perhaps" , "Having scored an advantage" , "Maybe person on horseback" , "Having an advantage (over another person)" , "slightly ahead in contest" .)