Artist beset by duke, one demanding women's rights (8)
I believe the answer is:
feminist
'one demanding women's rights' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'artist beset by duke' is the wordplay.
'artist' becomes 'emin' (Tracey Emin).
'beset by' means one lot of letters goes inside another ('beset' could historically mean 'cover').
'duke' becomes 'fist' (put up your dukes).
'emin' going inside 'fist' is 'FEMINIST'.
Can you help me to learn more?
(Other definitions for feminist that I've seen before include "I'm finest as activist in women's lib movement" , "I'm finest with supporter of women's lib" , "Mine's fit (anag.)" , "I'm finest (anag.)" , "Advocate of women's rights" .)