Arrogant at university? Shame! (6)
I believe the answer is:
uppity
'arrogant' is the definition.
(I've seen this before)
'at university? shame' is the wordplay.
'at university?' becomes 'up' (slang term meaning at university).
'shame' becomes 'pity' (synonyms).
'up'+'pity'='UPPITY'
(Other definitions for uppity that I've seen before include "Impertinent" , "'Self-important, overweening (6)'" , "Presumptuously arrogant" , "Cheeky or presumptuous" , "Informally presumptuous or self-important" .)