Start university getting into arrears (5)
I believe the answer is:
debut
'start' is the definition.
(debut is a kind of start)
'university getting into arrears' is the wordplay.
'university' becomes 'u'.
'getting into' is an insertion indicator.
'arrears' becomes 'debt' (I've seen this before).
'u' put within 'debt' is 'DEBUT'.
(Other definitions for debut that I've seen before include "Appear in public for the first time" , "First appearance in society" , "First appearence as of society girl" , "First attempt" , "Introduction" .)