Bachelor blessing primate (6)
I believe the answer is:
baboon
'primate' is the definition.
(baboon is a kind of primate)
'bachelor blessing' is the wordplay.
'bachelor' becomes 'BA' (abbreviation for Bachelor of Arts degree).
'blessing' becomes 'boon' (synonyms).
'ba'+'boon'='BABOON'
(Other definitions for baboon that I've seen before include "Large long-nosed Arabian or African monkey" , "Large long-nosed African or Asian monkey" , "Ground-living primate" , "Stupid person" , "Type of large monkey" .)