At university, correct and honest (7)
I believe the answer is:
upright
'honest' is the definition.
(I've seen this before)
'at university correct' is the wordplay.
'at university' becomes 'up' (to 'come up' is to arrive for term, e.g. at Oxford).
'correct' becomes 'right' (right can mean correct).
'up'+'right'='UPRIGHT'
'and' is the link.
(Other definitions for upright that I've seen before include "Honest (like a piano?)" , "Vertical, erect" , "Virtuous" , "with principle" , "extremely reliable?" .)