Lot upset — prelate ultimately managed church, providing open-mindedness (9)
I believe the answer is:
tolerance
'open-mindedness' is the definition.
(I've seen this before)
'lot upset prelate ultimately managed church' is the wordplay.
'upset' says the letters should be written in reverse.
'ultimately' suggests the final letters.
'managed' becomes 'ran' (both can mean organised or was in charge of).
'church' becomes 'CE' (abbreviation for Church of England).
The final letter of 'prelate' is 'e'.
'lot' backwards is 'tol'.
'tol'+'e'+'ran'+'ce'='TOLERANCE'
'providing' acts as a link.
(Other definitions for tolerance that I've seen before include "Ability to stomach (something)" , "Ability to be fair" , "Allowable variation (in size)" , "Amount of play" , "resignation" .)