Outlaw about to shout down a primate (6)
I believe the answer is:
baboon
'a primate' is the definition.
(I know that baboon is a type of Old World monkey)
'outlaw about to shout down' is the wordplay.
'outlaw' becomes 'ban' (banning is a kind of outlawing).
'about' is an insertion indicator.
'to shout down' becomes 'boo' (I am not sure about this - if you are sure you should believe this answer much more).
'ban' placed around 'boo' is 'BABOON'.
Can you help me to learn more?
(Other definitions for baboon that I've seen before include "Uncouth type" , "Stupid person" , "animal" , "clumsy uncouth person" , "wild swinger?" .)