The most common and most likely answer to this crossword clue is the 9 letter word CONFESSOR
I've seen this crossword clue in The Daily Telegraph
C
O
N
F
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More clues leading to the result CONFESSOR
Buddy explains!

The straight part
We know that "Priest perhaps" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case priest perhaps = confessor.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 CONFESSOR mean?
CONFESSOR noun- One who confesses faith in Christianity in the face of persecution, but who is not martyred.
- One who confesses to having done something wrong.
- A priest who hears confession and then gives absolution