Be smarter than old fool after university (6)
I believe the answer is:
outwit
'be smarter than' is the definition.
(I've seen this before)
'old fool after university' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'fool' becomes 'twit' (I've seen this before**).
'after' is a charade indicator (letters next to each other).
'university' becomes 'u'.
'twit' put after 'u' is 'utwit'.
'o'+'utwit'='OUTWIT'
(Other definitions for outwit that I've seen before include "To appear smarter" , "To fox" , "Gull" , "Get the better of by being smarter" , "Hoodwink" .)