Summary of part of competition at university (7)
I believe the answer is:
roundup
'summary' is the definition.
(roundup is a kind of summary)
'part of competition at university' is the wordplay.
'part of competition' becomes 'round' (as in a round in a contest).
'at university' becomes 'up' ('up' can mean studying at university).
'round'+'up'='ROUNDUP'
'of' is the link.
(Other definitions for roundup that I've seen before include "Summary (of events)" , "Gather into one place, animals or people" , "Gather together" , "Collection of facts" , "A systematic gathering" .)