Home counties girlfriend's demure (6)
I believe the answer is:
sedate
'demure' is the definition.
(thesaurus)
'home counties girlfriend's' is the wordplay.
'home counties' becomes 'se'.
'girlfriend' becomes 'date' (I've seen this in other clues).
'se'+'date'='SEDATE'
(Other definitions for sedate that I've seen before include "Dignified and sombre" , "Collected" , "Composed and staid" , "Quiet and dignified" , "Calm and dignified in manner" .)