Cleans grime off dairy product (6,5)
I believe the answer is:
single cream
'dairy product' is the definition.
(I've seen this before)
'cleans grime off' is the wordplay.
'off' indicates anagramming the letters.
'cleans'+'grime'='cleansgrime'
'cleansgrime' with letters rearranged gives 'SINGLE CREAM'.
(Other definitions for single cream that I've seen before include "emerges from the dairy" , "Dairy product; cleans grime (anagram)" , "food" .)