Cherish processed English cheese (8)
I believe the answer is:
cheshire
'cheese' is the definition.
(Cheshire cheese is an example)
'cherish processed english' is the wordplay.
'processed' indicates an anagram.
'english' becomes 'E' (abbreviation as in OED).
'cherish' with letters rearranged gives 'cheshir'.
'cheshir'+'e'='CHESHIRE'
(Other definitions for cheshire that I've seen before include "Crumbly cheese from northwest England" , "Cat with broad smile, from English county" , "English cheese or cat" , "division in England" , "part of England" .)