Let back in US college for supporting study (7)
I believe the answer is:
readmit
'let back in' is the definition.
(I've seen this before)
'us college for supporting study' is the wordplay.
'us college' becomes 'MIT' (I've seen this in other clues).
'for' is a charade indicator (letters next to each other) (I've seen this in other clues).
'supporting study' becomes 'read' (synonyms. I am not sure about the 'supporting' bit.).
'mit' after 'read' is 'READMIT'.
Can you help me to learn more?
(Other definitions for readmit that I've seen before include "Welcome back" , "Again accept" , "Let back in" , "Let in a second time" , "Allow back into" .)