Tune rewritten in hunt for singer (9)
I believe the answer is:
chanteuse
'singer' is the definition.
(French term for a female singer)
'tune rewritten in hunt' is the wordplay.
'rewritten' indicates an anagram.
'in' means one lot of letters goes inside another.
'hunt' becomes 'chase' (I've seen this in another clue).
'tune' anagrammed gives 'nteu'.
'nteu' placed inside 'chase' is 'CHANTEUSE'.
'for' acts as a link.
(Other definitions for chanteuse that I've seen before include "A French woman singer of popular ballads" , "She sings popular songs" , "Female cabaret singer" , "Female singer, in a nightclub perhaps" , "Tunes ache for this French woman singer" .)