Girl from Bognor, a hairdresser (5)
I believe the answer is:
norah
'girl' is the definition.
'from bognor a hairdresser' is the wordplay.
'from' indicates the answer is hidden within the clue.
'NORAH' is hidden in the letters of 'bognor a hairdresser'.
(Other definitions for norah that I've seen before include "Batty woman" , "Girl" , "Girl's name" .)