Resolved to live permanently with duke (7)
I believe the answer is:
settled
'resolved' is the definition.
(settling is a kind of resolving)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for settled that I've seen before include "Took up residence" , "Agreed; sorted" , "came to agreement" , "Sank or came to rest" , "no longer an issue" .)