Primate and bishop getting a blessing (6)
I believe the answer is:
baboon
'primate' is the definition.
(I know that baboon is a type of Old World monkey)
'bishop getting a blessing' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'getting' means one lot of letters go next to another.
'blessing' becomes 'boon' (synonyms).
'b'+'a'+'boon'='BABOON'
'and' is the link.
(Other definitions for baboon that I've seen before include "A large one of 17 across" , "Ground-living primate" , "Type of large monkey" , "Uncouth type" , "Large primate" .)