Preacher touring north finally rejected beer and cheese (11)
I believe the answer is:
wensleydale
'cheese' is the definition.
(I've seen this before)
'preacher touring north finally rejected beer' is the wordplay.
'preacher' becomes 'wesley' (I've seen this before).
'touring' is an insertion indicator (touring can mean going round).
'north' becomes 'N' (abbreviation).
'finally rejected beer' becomes 'dale' (I can't explain this - if you can you should give a lot more credence to this answer).
'wesley' enclosing 'n' is 'wensley'.
'wensley'+'dale'='WENSLEYDALE'
'and' acts as a link.
(Other definitions for wensleydale that I've seen before include "Say, we'll need (anag); a cheese" , "Type of white cheese" , "Yorkshire cheese" , "4 across" , "Wallace's favourite cheese" .)