Home counties girlfriend's demure (6)
I believe the answer is:
'demure' is the definition.
'home counties girlfriend's' is the wordplay.
'home counties' becomes 'se'.
'girlfriend' becomes 'date' (I've seen this in other clues).
(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" .)