Primate and bishop leading 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 leading a blessing' is the wordplay.
'leading' indicates taking the first letters.
'blessing' becomes 'boon' (synonyms).
The first letter of 'bishop' is 'b'.
'b'+'a'+'boon'='BABOON'
'and' acts as a link.
(Other definitions for baboon that I've seen before include "animal" , "Type of large monkey" , "Large long-nosed African or Asian monkey" , "clumsy uncouth person" , "wild swinger?" .)