Piano teacher holding back school (4)
I believe the answer is:
eton
'school' is the definition.
(famous UK public school)
'piano teacher holding back' is the wordplay.
'holding' indicates a hidden word.
'back' shows that the letters should be reversed in order.
'note' is hidden within 'piano teacher'.
'note' in reverse letter order is 'ETON'.
(Other definitions for eton that I've seen before include "Public school founded by Henry VI" , "Note sent up to English public school" , "Easy to understand" , "Independent school" , "Posh English school of note" .)