The rest live around university (7)
I believe the answer is:
residue
'the rest' is the definition.
(residue can mean the remains or rest of something)
'live around university' is the wordplay.
'live' becomes 'reside' (residing is a kind of living).
'around' is an insertion indicator.
'university' becomes 'u' (abbreviation for university).
'reside' placed around 'u' is 'RESIDUE'.
(Other definitions for residue that I've seen before include "Remains to be seen" , "Part remaining" , "Stuff left over" , "Leftovers" , "grounds" .)