Summary of stage of competition at university (5,2)
I believe the answer is:
round up
'summary' is the definition.
(I've seen this before)
'stage of competition at university' is the wordplay.
'stage of competition' becomes 'round' (I've seen this before).
'at university' becomes 'up' (slang term meaning at university).
'round'+'up'='ROUND-UP'
'of' acts as a link.
(Other definitions for round up that I've seen before include "Collect" , "Gather together" , "Summary" , "rally" , "herd" .)