A chit to take back to school (4)
I believe the answer is:
note
'a chit' is the definition.
(thesaurus)
'back to school' is the wordplay.
'back' says the letters should be written in reverse.
'to school' becomes 'eton' (famous UK public school).
'eton' back-to-front is 'NOTE'.
'to take' acts as a link.
(Other definitions for note that I've seen before include "Consequence" , "Memo; piano key" , "Detect and remember" , "Write down" , "Observe in Eton" .)