Musical character left cycling round upset old hag (5,4)
I believe the answer is:
tenor clef
'musical character' is the definition.
(symbol (character) in musical notation)
'left cycling round upset old hag' is the wordplay.
'cycling' is an anagram indicator.
'round' means one lot of letters goes inside another.
'upset' says the letters should be written in reverse.
'old hag' becomes 'crone' (I've seen this in another clue).
'crone' in reverse letter order is 'enorc'.
'left' with letters rearranged gives 'tlef'.
'tlef' going around 'enorc' is 'TENOR-CLEF'.
(Other definitions for tenor clef that I've seen before include "A stave marking for pitch" , "instruction for a musician" , "One on the staff" , "Character instructing musician" , "It has middle C on second- highest line" .)