Piece of music band advertise endlessly (4)
I believe the answer is:
opus
'piece of music' is the definition.
('opus' can be a synonym of 'piece of music')
'band advertise endlessly' is the wordplay.
'band' becomes 'o' (I've seen this in other clues).
'advertise' becomes 'push' ('push' can be a synonym of 'advertize').
'endlessly' means to remove the last letter.
'push' with its last letter removed is 'pus'.
'o'+'pus'='OPUS'
(Other definitions for opus that I've seen before include "Composer's work" , "Musical composition in the soup" , "Work (of a composer?)" , "Piece of music (with number)" , "Soup (anag.)" .)