The most common and most likely answer to this crossword clue is the 4 letter word LEVI
I've seen this crossword clue in Financial Times
L
E
V
I
More clues leading to the result LEVI
- Patriarch against wearing Hawaiian garland
- Priest in little village
- OT character to rise at the Tate?
- Priest very briefly appearing in garland
- Priest in short trousers?
- Scriptural character, one existing on bread abroad
- Singular trousers, apparently, for Jacob’s son
- Italian novelist found in simple village
- Coupleembraced for one of Strauss’s
- Figure in Genesis is vile, switching sides
Buddy explains!

The straight part
We know that "Priest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case priest = levi.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.