College sends back a short letter (4)
I believe the answer is:
eton
'college' is the definition.
(Eton College, English private school)
'back a short letter' is the wordplay.
'back' says the letters should be written in reverse.
'a short letter' becomes 'note' ('note' can be a synonym of 'short letter').
'note' written backwards gives 'ETON'.
'sends' is the link.
(Other definitions for eton that I've seen before include "Famous college" , "Note sent up to English public school" , "Easy to understand" , "Berks college" , "Berkshire public school" .)