Piece of music written up for school (4)
I believe the answer is:
eton
'school' is the definition.
(famous UK public school)
'piece of music written up' is the wordplay.
'piece of music' becomes 'note' (I've seen this before).
'written up' says the letters should be written in reverse.
'note' back-to-front is 'ETON'.
'for' is the link.
(Other definitions for eton that I've seen before include "College, collar or crop" , "Easy to understand" , "Collar - crop - jacket - school" , "College in Berkshire" , "Kind of collar or jacket (worn at college?)" .)