The remainder live outside the university (7)
I believe the answer is:
residue
'the remainder' is the definition.
(residue means a remainder or remains)
'live outside the university' is the wordplay.
'live' becomes 'reside' (synonyms).
'outside' means one lot of letters goes inside another (some letters go outside others).
'the university' becomes 'U' (abbreviation as in UMass).
'reside' enclosing 'u' is 'RESIDUE'.
(Other definitions for residue that I've seen before include "Lees, dregs" , "Material left" , "Leftovers" , "Dire use of what is left over" , "Matter left behind after other parts have been taken away" .)