Nanny's relations supply the material (8)
I believe the answer is:
goatskin
'the material' is the definition.
'nanny's relations' is the wordplay.
'nanny's' becomes 'goats' (nanny is a female goat).
'relations' becomes 'kin' (I've seen this before).
'goats'+'kin'='GOATSKIN'
'supply' is the link.
(Other definitions for goatskin that I've seen before include "Leather - wine holder of old" , "Leather from nanny or billy?" , "Type of leather - a song kit (anag)" , "Billy's hide?" , "Hide Billy or Nanny" .)