Veggie fan? That woman’s drill involves one source of veganism (9)
I believe the answer is:
herbivore
'veggie fan?' is the definition.
(animal which eats vegetables)
'woman's drill involves one source of veganism' is the wordplay.
'woman's' becomes 'her' (belonging to a woman).
'drill' becomes 'bore' (synonyms).
'involves' means one lot of letters goes inside another.
'one' becomes 'I' (Roman numeral).
'source of' suggests taking the first letters.
The initial letter of 'veganism' is 'v'.
'i'+'v'='iv'
'bore' placed around 'iv' is 'bivore'.
'her'+'bivore'='HERBIVORE'
'that' is the link.
(Other definitions for herbivore that I've seen before include "Plant eater" , "Grass-eating animal" , "no meat-eater" .)