Quality woolly attire covering on the other hand (9)
I believe the answer is:
attribute
'quality' is the definition.
(I've seen this before)
'woolly attire covering on the other hand' is the wordplay.
'woolly' is an anagram indicator (I've seen this in other clues).
'covering' is an insertion indicator.
'on the other hand' becomes 'but' (I've seen this before).
'attire' anagrammed gives 'attrie'.
'attrie' enclosing 'but' is 'ATTRIBUTE'.
(Other definitions for attribute that I've seen before include "Credit - property" , "Assign" , "charge" , "Quality characteristic of person or thing" , "Character" .)