Let in again to study with Cambridge University (7)
I believe the answer is:
readmit
'let in again' is the definition.
('admit' can be a synonym for 'let in' so perhaps 'readmit' is OK for 'let in again')
'study with cambridge university' is the wordplay.
'study' becomes 'read' ('read' can be a synonym of 'study').
'with' says to put letters next to each other.
'cambridge university' becomes 'mit' (Massachusetts Institute of Technology in Cambridge).
'read'+'mit'='READMIT'
'to' is the link.
(Other definitions for readmit that I've seen before include "Let in a second time" , "Let back in" , "Welcome back" , "Allow back into" , "Again accept" .)