Sent girl out for hair styling (8)
I believe the answer is:
ringlets
'hair styling' is the definition.
(I know that ringlets is a hair styling)
'sent girl out' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'sent'+'girl'='sentgirl'
'sentgirl' with letters rearranged gives 'RINGLETS'.
'for' acts as a link.
(Other definitions for ringlets that I've seen before include "Locks" , "Spiral curls" , "Sterling sort of curls" , "Curls, of Irish dancers say" , "Curls or tendrils" .)