Carry on upsetting priests (7)
I believe the answer is:
persist
'carry on' is the definition.
(to persist is to carry on with something)
'upsetting priests' is the wordplay.
'upsetting' indicates an anagram.
'priests' is an anagram of 'PERSIST'.
(Other definitions for persist that I've seen before include "Continue to exist" , "Go on and on" , "Continue despite opposition" , "Continue (in spite of difficulties)" , "Stick with" .)