Lively chat about a bishop's complaint (7)
I believe the answer is:
catarrh
'complaint' is the definition.
(medical complaint)
'lively chat about a bishop's' is the wordplay.
'lively' is an anagram indicator (I've seen this in other clues).
'about' is an insertion indicator.
'bishop' becomes 'rr' (abbreviation for Right Reverend).
'chat' with letters rearranged gives 'cath'.
'a'+'rr'='arr'
'cath' enclosing 'arr' is 'CATARRH'.
(Other definitions for catarrh that I've seen before include "cold symptom" , "Problem with cold" , "Arch rat with inflammation of mucous membrane" , "Nasal build-up" , "Nasal congestion" .)