Passage emerging from former church run by discontented priest (7)
I believe the answer is:
excerpt
'passage' is the definition.
(excerpt is a kind of passage)
'former church run by discontented priest' is the wordplay.
'former' becomes 'ex' (prefix meaning former or onetime).
'church' becomes 'ce' (Church of England).
'run' becomes 'r' (cricket abbreviation).
'by' means one lot of letters go next to another.
'discontented' says to hollow out the word (remove centre letters) (the word's contents are removed).
'priest' with its centre taken out is 'pt'.
'ex'+'ce'+'r'+'pt'='EXCERPT'
'emerging from' acts as a link.
(Other definitions for excerpt that I've seen before include "Selected passage from larger work" , "Passage from book, play etc" , "Just a few words" , "Literary taste" , "bit of work" .)