Pacify primate eating vegetables (7)
I believe the answer is:
appease
'pacify' is the definition.
(synonyms)
'primate eating vegetables' is the wordplay.
'primate' becomes 'ape' (large primate).
'eating' means one lot of letters goes inside another.
'vegetables' becomes 'peas' (peas are a type of vegetable).
'ape' enclosing 'peas' is 'APPEASE'.
(Other definitions for appease that I've seen before include "Pacify with concessions" , "Placate (someone) with concessions" , "Make calm by offering concessions" , "Placate by making concessions" , "Mollify or calm by making concessions" .)