Excuse made by average teacher at university (6)
I believe the answer is:
pardon
'excuse' is the definition.
('pardon' can be a synonym of 'excuse')
'by average teacher at university' is the wordplay.
'by' means one lot of letters go next to another.
'average' becomes 'par' (I've seen this before).
'teacher at university' becomes 'don'.
'par' put next to 'don' is 'PARDON'.
'made' acts as a link.
(Other definitions for pardon that I've seen before include "Forgive; come again?" , "Forgiveness - I beg yours" , "What was that you said" , "Grant forgiveness" , "Allow to go unpunished" .)