Pacify primate with vegetables (7)
I believe the answer is:
appease
'pacify' is the definition.
('appease' can be a synonym of 'pacify')
'primate with vegetables' is the wordplay.
'primate' becomes 'ape' (I've seen this before).
'with' is an insertion indicator.
'vegetables' becomes 'peas' (I've seen this before).
'ape' placed around 'peas' is 'APPEASE'.
(Other definitions for appease that I've seen before include "Mollify or calm by making concessions" , "Pacify with concessions" , "Placate (someone) with concessions" , "Placate by making concessions" , "Satisfy demands by making concessions" .)