Memo backing famous school (4)
I believe the answer is:
note
'memo' is the definition.
(I've seen this before)
'backing famous school' is the wordplay.
'backing' says the letters should be written backwards.
'famous school' becomes 'eton' (English private school).
'eton' reversed gives 'NOTE'.
(Other definitions for note that I've seen before include "Observe the musical pitch." , "Short message; tone" , "Observe, record" , "Heed; short letter" , "Fiver, say" .)