Preacher entertaining northern duke with beer and cheese (11)
I believe the answer is:
wensleydale
'cheese' is the definition.
(thesaurus)
'preacher entertaining northern duke with beer' is the wordplay.
'preacher' becomes 'wesley' (I've seen this before).
'entertaining' means one lot of letters goes inside another.
'northern' becomes 'n' (abbreviation e.g. N. Ireland).
'duke with' becomes 'd' (I can't justify this - if you can you should give a lot more credence to this answer).
'beer' becomes 'ale' (I've seen this before).
'wesley' enclosing 'n' is 'wensley'.
'wensley'+'d'+'ale'='WENSLEYDALE'
'and' acts as a link.
(Other definitions for wensleydale that I've seen before include "4 across" , "White crumbly variety of cheese" , "Type of white cheese" , "Wallace's favourite cheese" , "Yorkshire cheese" .)