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