Silk getting terribly fat on cheese (7)
I believe the answer is:
taffeta
'silk' is the definition.
(I've seen this before)
'terribly fat on cheese' is the wordplay.
'terribly' is an anagram indicator.
'on' is a charade indicator (letters next to each other).
'cheese' becomes 'feta' (type of cheese).
'fat' anagrammed gives 'taf'.
'taf'+'feta'='TAFFETA'
'getting' acts as a link.
(Other definitions for taffeta that I've seen before include "Stiff shiny material" , "A shiny silklike fabric" , "Thin glossy silk fabric" , "cloth" , "Thin crisp lustrous silk" .)