Consume the greater part (3)
I believe the answer is:
eat
'consume' is the definition.
(eating is a kind of consuming)
'greater part' is the wordplay.
'part' indicates the answer is hidden within the clue.
'EAT' is hidden within 'greater'.
'the' is the link.
(Other definitions for eat that I've seen before include "Corrode" , "get stuck in" , "Have 23d [MEAL]" , "Use a knife and fork" , "Devour" .)