His home, with King and Duke, possibly a hereditary state (9)

I believe the answer is:
sheikhdom
'a hereditary state' is the definition.
The answer and definition can be both locations as well as being singular nouns.
Maybe there's a link between them I don't understand?
'his home with king and duke possibly' is the wordplay.
'with' is a charade indicator (letters next to each other).
'king' becomes 'K' (chess abbreviation).
'and' says to put letters next to each other.
'duke' becomes 'd' (abbreviation).
'possibly' indicates an anagram.
'his'+'home'+'k'+'d'='hishomekd'
'hishomekd' anagrammed gives 'SHEIKHDOM'.
Can you help me to learn more?
(Other definitions for sheikhdom that I've seen before include "Qatar perhaps" , "Arab chief's territory" , "Muslim leader in his territory" .)
