Rest live around university (7)
I believe the answer is:
residue
'rest' is the definition.
(residue can mean the remains or rest of something)
'live around university' is the wordplay.
'live' becomes 'reside' (synonyms).
'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 "waste" , "Matter left behind after other parts have been taken away" , "What remains of something" , "Something remaining" , "Stuff left over" .)