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' says to take the final letters.
The last letter of 'take' is 'e'.
'e'+'to'='eto'
'n' put 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" .)