Bill comes up with a new coil of fabric (6)
I believe the answer is:
calico
'fabric' is the definition.
(I know that calico is a type of fabric)
'bill comes up with a new coil' is the wordplay.
'bill' becomes 'ac' (short for account).
'comes up' shows that the letters should be reversed in order (in a down clue, letters go up).
'with' says to put letters next to each other.
'a new' indicates anagramming the letters.
'ac' written backwards gives 'ca'.
'coil' anagrammed gives 'lico'.
'ca'+'lico'='CALICO'
'of' acts as a link.
(Other definitions for calico that I've seen before include "Coarse printed cotton cloth" , "Coarse cloth with a bright print" , "Unbleached sixteen down cloth" , "Cotton cloth or fabric" , "White cotton fabric" .)