Let back in to US university after study (7)
I believe the answer is:
readmit
'let back in' is the definition.
(I've seen this before)
'us university after study' is the wordplay.
'us university' becomes 'MIT' (Massachusetts Institute of Technology).
'after' means one lot of letters go next to another.
'study' becomes 'read' (synonyms).
'mit' after 'read' is 'READMIT'.
'to' is the link.
(Other definitions for readmit that I've seen before include "Take in again" , "Dear Tim (anag.)" , "Allow back into" , "Again accept" , "Let in a second time" .)