Note in case director quit (6)
I believe the answer is:
ceased
'quit' is the definition.
(I've seen this in another clue)
'note in case director' is the wordplay.
'note' becomes 'e' (musical note).
'in' indicates putting letters inside.
'director' becomes 'd'.
'e' put into 'case' is 'cease'.
'cease'+'d'='CEASED'
(Other definitions for ceased that I've seen before include "Terminated" , "Stopped, ended" , "Finished" , "Stopped, desisted" , "Stopped or discontinued" .)