Chill for a long time around university (4)
I believe the answer is:
ague
'chill' is the definition.
(synonyms)
'long time around university' is the wordplay.
'long time' becomes 'age' (an age is a period of time).
'around' indicates putting letters inside.
'university' becomes 'U' (abbreviation for university).
'age' going around 'u' is 'AGUE'.
'for a' is the link.
(Other definitions for ague that I've seen before include "Malarial fever or fit of shivering" , "Old word for fever" , "Acute fever; shivering fit" , "Fit of shivering and shaking" , "attack" .)