Arise as priest's last organised part of church (9)
I believe the answer is:
transpire
'arise' is the definition.
(thesaurus)
'priest's last organised part of church' is the wordplay.
'last' indicates one should take the final letters.
'organised' becomes 'ran' (I've seen this before).
'part of church' becomes 'spire'.
The last letter of 'priest' is 't'.
't'+'ran'+'spire'='TRANSPIRE'
'as' acts as a link.
(Other definitions for transpire that I've seen before include "Turn out" , "exhale" , "Terrapins (anag)" , "Lose water vapour" , "Become known about terrapins" .)