Remainder to lodge round university (7)
I believe the answer is:
residue
'remainder' is the definition.
('residue' can be a synonym of 'remainder')
'lodge round university' is the wordplay.
'lodge' becomes 'reside' (I've seen this before**).
'round' is an insertion indicator.
'university' becomes 'u'.
'reside' going around 'u' is 'RESIDUE'.
'to' acts as a link.
(Other definitions for residue that I've seen before include "Something left over" , "What's left" , "Stuff left over" , "Surplus" , "Part remaining" .)