Fine English girl's hat (6)
I believe the answer is:
fedora
'hat' is the definition.
(fedora is a kind of hat)
'fine english girl's' is the wordplay.
'fine' becomes 'f' (abbreviation).
'english' becomes 'e' (abbreviation).
'girl' becomes 'dora' (**).
'f'+'e'+'dora'='FEDORA'
(Other definitions for fedora that I've seen before include "Brimmed hat with creased crown" , "Felt hat dented lengthways" , "Type of hat" , "top fashion" , "Felt hat with a creased crown" .)