Entertaining duke, newspaper proprietor provides evening drink (9)
I believe the answer is:
sundowner
'evening drink' is the definition.
(I've seen this before)
'entertaining duke newspaper proprietor' is the wordplay.
'entertaining' is an insertion indicator.
'duke' becomes 'd'.
'newspaper' becomes 'sun' (I've seen this before).
'proprietor' becomes 'owner' ('owner' can be a synonym of 'proprietor').
'sun'+'owner'='sunowner'
'd' put into 'sunowner' is 'SUNDOWNER'.
'provides' acts as a link.
(Other definitions for sundowner that I've seen before include "Victorian tramp?" , "Twilight drink" , "Evening drink" , "Tramp (Australian) - drink (British)" , "cocktail?" .)