"Mean" means paring the cheese (8)
I believe the answer is:
parmesan
'cheese' is the definition.
(Parmesan is an example)
'mean means paring' is the wordplay.
I cannot really understand how this works, but
'mean' could be 'par' (average score on a golf course) and 'par' is present in the answer.
an anagram of 'means' is 'mesan' which is located in the answer.
No letters remain.
This explanation may well be incorrect...
'the' is the link.
Can you help me to learn more?
(Other definitions for parmesan that I've seen before include "Italian 8 across" , "that grates" , "Italian cheese, often grated" , "Dry sharp-flavoured Italian cheese" , "Spearman (anag) - cheese" .)