Material in fat turned up on some Greek cheese (7)
I believe the answer is:
taffeta
'material' is the definition.
(I know that taffeta is a type of material)
'fat turned up on some greek cheese' is the wordplay.
'turned up' says the letters should be written backwards.
'on' is a charade indicator (letters next to each other).
'some greek cheese' becomes 'feta' (I've seen this in another clue).
'fat' back-to-front is 'taf'.
'taf'+'feta'='TAFFETA'
'in' acts as a link.
(Other definitions for taffeta that I've seen before include "Fabric -- a fat eft (anag)" , "Shiny silk with a crisp texture" , "silky stuff" , "Thin silky material" , "Crisp, smooth, lustrous fabric" .)