Character to sing about hairstyle (6)
I believe the answer is:
mullet
'hairstyle' is the definition.
(I know that mullet is a hairstyle)
'character to sing about' is the wordplay.
'character' becomes 'mu' (Greek letter).
'to sing' becomes 'tell' (sing can mean to tell the authorities something).
'about' shows that the letters should be reversed in order.
'tell' in reverse letter order is 'llet'.
'mu'+'llet'='MULLET'
(Other definitions for mullet that I've seen before include "swimmer" , "Fish - bad haircut" , "Starfish" , "Fish; man's hair style" , "Barnet?" .)