Remainder live around university (7)
I believe the answer is:
residue
'remainder' is the definition.
('residue' can be a synonym of 'remainder')
'live around university' is the wordplay.
'live' becomes 'reside' (residing is a kind of living).
'around' means one lot of letters goes inside another.
'university' becomes 'u'.
'reside' placed around 'u' is 'RESIDUE'.
(Other definitions for residue that I've seen before include "What's left" , "Stuff left over" , "grounds" , "Net worth of estate" , "Surplus" .)