A note to take back to school (4)
I believe the answer is:
eton
'school' is the definition.
(famous UK public school)
'a note to take back to' is the wordplay.
'a note' becomes 'n' (abbreviation).
'to' says to put letters next to each other (I've seen this in other clues).
'back' suggests the final letters (the letter at the back).
The last letter of 'take' is 'e'.
'e'+'to'='eto'
'n' after 'eto' is 'ETON'.
(Other definitions for eton that I've seen before include "Place for learning" , "academic institution" , "School - note (anag)" , "Note sent up to English public school" , "Famous college" .)