Archbishops in particular ate seconds (8)
I believe the answer is:
primates
'archbishops' is the definition.
(I've seen this in another clue)
'particular ate seconds' is the wordplay.
'particular' becomes 'prim' (prim can mean precise or particular).
'seconds' becomes 's' (abbreviation).
'prim'+'ate'+'s'='PRIMATES'
'in' acts as a link.
(Other definitions for primates that I've seen before include "Animals including monkeys and apes" , "Apes; bishops" , "Lemurs, apes, men, etc." , "some leading churchmen" , "Archbishops or apes" .)