Dregs live around university (7)
I believe the answer is:
residue
'dregs' is the definition.
(thesaurus)
'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' going around 'u' is 'RESIDUE'.
(Other definitions for residue that I've seen before include "grounds" , "Material left" , "What's left" , "What remains of something" , "Part remaining" .)