Bishop of Rome and Priest having acceptable disagreement (7)
I believe the answer is:
pontiff
'bishop of rome' is the definition.
(I've seen this in another clue)
'priest having acceptable disagreement' is the wordplay.
'priest' becomes 'p' (ecclesiastical abbreviation).
'having' means one lot of letters go next to another.
'acceptable' becomes 'on' (as opposed to not on, unacceptable).
'disagreement' becomes 'tiff' (tiff is a kind of disagreement).
'p'+'on'+'tiff'='PONTIFF'
'and' acts as a link.
(Other definitions for pontiff that I've seen before include "Head of the Roman Catholic church" , "High-priest" , "Bishop" , "Title for a pope" , "Religious leader" .)