Archbishop’s formal tea arrangement (7)
I believe the answer is:
primate
'archbishop's' is the definition.
(I've seen this before)
'formal tea arrangement' is the wordplay.
'formal' becomes 'prim' (I've seen this before).
'arrangement' is an anagram indicator.
'tea' with letters rearranged gives 'ate'.
'prim'+'ate'='PRIMATE'
(Other definitions for primate that I've seen before include "E.g. monkey, ape, archbishop" , "Archbishop - monkey, perhaps" , "Chief priest" , "senior clergyman" , "senior cleric" .)