Duke having a tea in a country house (5)
I believe the answer is:
dacha
'a country house' is the definition.
(dacha is a kind of country house)
'duke having a tea' is the wordplay.
'duke' becomes 'd'.
'having' means one lot of letters go next to another.
'tea' becomes 'cha' (cha is a type of tea).
'd'+'a'+'cha'='DACHA'
'in' acts as a link.
(Other definitions for dacha that I've seen before include "Country home in Russia" , "A Russian country cottage" , "summer house" , "Russian second home" , "Russian's second home in the country" .)