A new gender identity in this part of the country? (9)
I believe the answer is:
middlesex
'identity in this part of the country?' is the definition.
The definition suggests a singular noun which matches the answer.
'a new gender' is the wordplay.
'a new' becomes 'middle' (I can't explain this - if you can you should give a lot more credence to this answer).
'gender' becomes 'sex' (synonyms).
'middle'+'sex'='MIDDLESEX'
(Other definitions for middlesex that I've seen before include "Cricketers" , "Cricketing county" .)