Funny priests carry on (7)
I believe the answer is:
persist
'carry on' is the definition.
(to persist is to carry on with something)
'funny priests' is the wordplay.
'funny' indicates anagramming the letters.
'priests' is an anagram of 'PERSIST'.
(Other definitions for persist that I've seen before include "Go on and on" , "Pursue course doggedly" , "Show doggedness" , "Keep trying" , "Continue to exist" .)