Remainder live outside university (7)
I believe the answer is:
residue
'remainder' is the definition.
(residue means a remainder or remains)
'live outside university' is the wordplay.
'live' becomes 'reside' (synonyms).
'outside' indicates putting letters inside (some letters go outside others).
'university' becomes 'U' (abbreviation for university).
'reside' placed around 'u' is 'RESIDUE'.
(Other definitions for residue that I've seen before include "balance" , "What is left, maybe dregs" , "Small amount remaining" , "Remaining portion" , "Remains to be seen" .)