Country home of duke, a fellow quietly forgotten (5)
I believe the answer is:
dacha
'country home' is the definition.
'dacha' can be an answer for 'home' (I have seen 'Russian home' mean 'dacha' so perhaps 'home' could also mean 'dacha'). I am unsure of the 'country' bit.
'of duke a fellow quietly forgotten' is the wordplay.
'of duke' becomes 'da' (I can't explain this - if you can you should give a lot more credence to this answer).
'a fellow' becomes 'chap' (both can mean a man).
'quietly' becomes 'p' (p for piano and quiet).
'forgotten' suggests deleting specific letters.
'chap' with 'p' removed is 'cha'.
'da'+'cha'='DACHA'
Can you help me to learn more?
(Other definitions for dacha that I've seen before include "Russian holiday cottage" , "Russian second home" , "Russian retreat" , "Russian country home" , "Russian villa" .)