Tricky question trapping university show-off (6)
I believe the answer is:
poseur
'show-off' is the definition.
(poseur is a kind of show-off)
'tricky question trapping university' is the wordplay.
'tricky question' becomes 'poser' (I've seen this before).
'trapping' means one lot of letters goes inside another.
'university' becomes 'u'.
'poser' enclosing 'u' is 'POSEUR'.
(Other definitions for poseur that I've seen before include "Person who's affected" , "One seeking to impress others with affected style" , "One who strikes attitudes, a phoney" , "Pretentious chap" , "Person habitually pretending to be something he is not" .)