Angora worn containing unknown material (7)
I believe the answer is:
organza
'material' is the definition.
(organza is a kind of material)
'angora worn containing unknown' is the wordplay.
'worn' is an anagram indicator (worn can mean damaged).
'containing' means one lot of letters goes inside another.
'unknown' becomes 'z' (algebra).
'angora' anagrammed gives 'organa'.
'organa' placed around 'z' is 'ORGANZA'.
(Other definitions for organza that I've seen before include "Transparent silky material" , "Thin stiff natural or synthetic fabric" , "Stuff" , "Thin material" , "Silk (or silk-like) fabric" .)