Material with back fat: cheese (7)
I believe the answer is:
taffeta
'material' is the definition.
(taffeta is a kind of material)
'with back fat cheese' is the wordplay.
'with' says to put letters next to each other.
'back' is a reversal indicator.
'cheese' becomes 'feta' (type of cheese).
'fat' reversed gives 'taf'.
'taf' put next to 'feta' is 'TAFFETA'.
(Other definitions for taffeta that I've seen before include "Fabric -- a fat eft (anag)" , "Thin glossy silk fabric" , "fine material for dressing" , "Crisp, smooth, lustrous fabric" , "Lustrous silky fabric" .)