The most common and most likely answer to this crossword clue is the 9 letter word PRIESTESS
I've seen this crossword clue in The Times
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More clues leading to the result PRIESTESS
Buddy explains!
The straight part
We know that "Non-Christian minister" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case non-christian minister = priestess.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 PRIESTESS mean?
PRIESTESS noun- A woman with religious duties and responsibilities in certain non-Christian religions.
- A female Christian priest or minister, typically in a Protestant, Old Catholic, or independent Catholic denomination.
- A priest’s wife.
- To oversee (a pagan ceremony, etc.) as priestess.