Pacify primate eating some veg (7)
I believe the answer is:
appease
'pacify' is the definition.
(synonyms)
'primate eating some veg' is the wordplay.
'primate' becomes 'ape' (large primate).
'eating' is an insertion indicator.
'some veg' becomes 'peas' (I can't explain this - if you can you should give a lot more credence to this answer).
'ape' placed around 'peas' is 'APPEASE'.
Can you help me to learn more?
(Other definitions for appease that I've seen before include "Mollify or calm by making concessions" , "Mollify, placate" , "Quiet" , "Propitiate by concessions" , "Calm, pacify, placate" .)