Bill comes up with new coil of fabric (6)
I believe the answer is:
calico
'fabric' is the definition.
(calico is a kind of fabric)
'bill comes up with new coil' is the wordplay.
'bill' becomes 'ac'.
'comes up' says the letters should be written backwards.
'with' says to put letters next to each other.
'new' indicates an anagram.
'ac' in reverse letter order is 'ca'.
'coil' is an anagram of 'lico'.
'ca'+'lico'='CALICO'
'of' is the link.
(Other definitions for calico that I've seen before include "Coarse printed cotton cloth" , "Plain cotton cloth, white or unbleached" , "Given material for dress" , "Cotton cloth or fabric" , "Type of cotton cloth" .)