Bishop with a blessing for primate (6)
I believe the answer is:
baboon
'primate' is the definition.
(baboon is a kind of primate)
'bishop with a blessing' is the wordplay.
'bishop' becomes 'b' (abbreviation used in chess).
'with' says to put letters next to each other.
'blessing' becomes 'boon' ('boon' can be a synonym of 'blessing').
'b'+'a'+'boon'='BABOON'
'for' acts as a link.
(Other definitions for baboon that I've seen before include "A large one of 17 across" , "clumsy uncouth person" , "Ground-living primate" , "Type of large monkey" , "Large long-nosed African or Asian monkey" .)