Female cutting inch of woven fabric (7)
I believe the answer is:
chiffon
'fabric' is the definition.
(chiffon is a kind of fabric)
'female cutting inch of woven' is the wordplay.
'female' becomes 'f' (abbreviation).
'cutting' indicates putting letters inside (some letters cut their way into a word).
'woven' indicates an anagram.
'inch'+'of'='inchof'
'inchof' anagrammed gives 'chifon'.
'f' going into 'chifon' is 'CHIFFON'.
(Other definitions for chiffon that I've seen before include "Fine (semi)transparent fabric" , "Sheer silk or rayon fabric" , "Thin light fabric" , "Fine material" , "Fine, near-transparent fabric" .)