Formidable woman writer, one with blue veins (10)
I believe the answer is:
gorgonzola
'one with blue veins' is the definition.
(blue cheese)
'formidable woman writer' is the wordplay.
'formidable woman' becomes 'gorgon' (type of mythological being).
'writer' becomes 'Zola' (Zola is an example).
'gorgon'+'zola'='GORGONZOLA'
(Other definitions for gorgonzola that I've seen before include "Italian town" , "Big cheese" , "Blue-veined cheese" , "Italian blue cheese" .)