Grey coat designed in class (8)
I believe the answer is:
category
'class' is the definition.
(I know that class can be written as category)
'grey coat designed' is the wordplay.
'designed' indicates an anagram (designed with the letters).
'grey'+'coat'='greycoat'
'greycoat' is an anagram of 'CATEGORY'.
'in' is the link.
(Other definitions for category that I've seen before include "Class of grey coat" , "Grey coat (anag.)" , "Genre" , "Class of grey-coat" , "Type" .)