The estate is run down, people say (7)
I believe the answer is:
demesne
'the estate' is the definition.
(synonyms)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for demesne that I've seen before include "Seed men (anag) -- land attached to a property and retained for the owner's personal use" , "Large landed property" , "Extensive landed property" , "Landed property used by the owner - needs me (anag)" , "Seed men on landed estate" .)