Female cutting inch of woven material (7)
I believe the answer is:
chiffon
'material' is the definition.
(I know that chiffon is a type of material)
'female cutting inch of woven' is the wordplay.
'female' becomes 'f' (abbreviation).
'cutting' means one lot of letters goes inside another (some letters cut their way into a word).
'woven' indicates anagramming the letters.
'inch'+'of'='inchof'
'inchof' anagrammed gives 'chifon'.
'f' put inside 'chifon' is 'CHIFFON'.
(Other definitions for chiffon that I've seen before include "Thin light fabric" , "Sheer silk or rayon fabric" , "Fine material" , "Fine, near-transparent fabric" , "dress material" .)