The most common and most likely answer to this crossword clue is the 9 letter word DEFROCKED
I've seen this crossword clue in The Guardian
D
E
F
R
O
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D
Buddy explains!

The straight part
We know that "No longer a priest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case no longer a priest = defrocked.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does DEFROCKED mean?
DEFROCKED verb- To divest of a frock.
- To formally remove the rights and authority of a member of the clergy.
- (by extension) To formally remove the rights and authority of someone, e.g. a government official or a medical practitioner.