Map quite possibly shows famous Kent country house (9)
I believe the answer is:
chartwell
'famous kent country house' is the definition.
I know nothing about this answer so I can't tell whether this works.
'map quite possibly' is the wordplay.
'map' becomes 'chart' (chart is a kind of map).
'quite possibly' becomes 'well'.
'chart'+'well'='CHARTWELL'
'shows' is the link.
Can you help me to learn more?
(Other definitions for chartwell that I've seen before include "Winston Churchill's Kent home" , "Churchill's place?" .)