Agree to adopt vessel unknown by European primate (10)
I believe the answer is:
chimpanzee
'primate' is the definition.
(chimpanzee is a kind of primate)
'agree to adopt vessel unknown by european' is the wordplay.
'agree' becomes 'chime'.
'to adopt' means one lot of letters goes inside another.
'vessel' becomes 'pan' (vessel or container for cooking).
'unknown' becomes 'z' (algebra).
'by european' becomes 'e' (abbreviation e.g. EU. I am not sure about the 'by' bit.).
'pan'+'z'='panz'
'chime' going around 'panz' is 'chimpanze'.
'chimpanze'+'e'='CHIMPANZEE'
(Other definitions for chimpanzee that I've seen before include "animal" , "Anthropoid ape" , "Primate" , "Intelligent ape" , "Close relative of man" .)