Let in again to study with Cambridge college (7)
I believe the answer is:
readmit
'let in again' is the definition.
(I've seen this before)
'study with cambridge college' is the wordplay.
'study' becomes 'read' ('read' can be a synonym of 'study').
'with' says to put letters next to each other.
'cambridge college' becomes 'mit' (Massachusetts Institute of Tech. in Cambridge, MA).
'read'+'mit'='READMIT'
'to' is the link.
(Other definitions for readmit that I've seen before include "Welcome back" , "Dear Tim (anag.)" , "Let in a second time" , "Let back in" , "Allow back into" .)