Remains in lodge outside university (7)
I believe the answer is:
residue
'remains' is the definition.
(I've seen this before)
'lodge outside university' is the wordplay.
'lodge' becomes 'reside' (I've seen this before).
'outside' indicates putting letters inside.
'university' becomes 'u' (abbreviation for university).
'reside' placed around 'u' is 'RESIDUE'.
'in' acts as a link.
(Other definitions for residue that I've seen before include "grounds" , "Lees, dregs" , "Part remaining" , "Something left over" , "Something remaining" .)