The most common and most likely answer to this crossword clue is the 8 letter word HIERATIC
I've seen this crossword clue in Financial Times
H
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The straight part
We know that "of priests" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case of priests = hieratic.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 HIERATIC mean?
HIERATIC noun- A writing system used in pharaonic Egypt that was developed alongside the hieroglyphic system, primarily written in ink with a reed brush on papyrus, allowing scribes to write quickly without resorting to the time consuming hieroglyphs.
- Of or pertaining to priests, especially pharaonic priests of Ancient Egypt.
- Of or pertaining to the cursive writing system that developed alongside the hieroglyphic system as its ordinary handwritten counterpart.
- Extremely stylized, restrained or formal; adhering to fixed types or methods; severe in emotional import.