Country house: term for family area (5)

I believe the answer is:

kenya

I'm a little stuck... Click here to teach me more about this clue!

'country' is the definition.
(I know that Kenya is a country)

I cannot understand how the remainder of the clue works.

(Other definitions for kenya that I've seen before include "Kikuyus' country" , "East African country" , "East African nation" , "Republic in East Africa" , "Its capital is Nairobi" .)

I've seen this clue in The Sunday Times and The Times.

Want a hint initially instead of a full solution? Install my app