British bishops into beer talk incessantly (6)
I believe the answer is:
babble
'talk incessantly' is the definition.
(I've seen this before)
'british bishops into beer' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'bishops' becomes 'bb' (a chess abbreviation for bishop written twice).
'into' is an insertion indicator.
'beer' becomes 'ale' (type of beer).
'bb' put within 'ale' is 'abble'.
'b'+'abble'='BABBLE'
(Other definitions for babble that I've seen before include "Meaningless noise" , "Chatter on like murmuring brook" , "Continuous noisy talk" , "Rapid and incomprehensible talk" , "Utter gibberish" .)