Duke not stuffy with fellow member, a milk producer (5,4)
I believe the answer is:
dairy farm
'a milk producer' is the definition.
(I've seen this in another clue)
'duke not stuffy with fellow member' is the wordplay.
'duke' becomes 'd' (abbreviation).
'not stuffy' becomes 'airy' (I've seen this in another clue).
'with' means one lot of letters go next to another.
'fellow' becomes 'f' (abbreviation - of a society etc.).
'member' becomes 'arm' (member can mean a limb).
'd'+'airy'+'f'+'arm'='DAIRY FARM'
(Other definitions for dairy farm that I've seen before include "Milk-producing concern" , "rural building" , "Supplier of milk products" , "cheese-shop supplier" , "Cattle are kept for milk here" .)