The most common and most likely answer to this crossword clue is the 6 letter word VICARS
I've seen this crossword clue in Financial Times
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More clues leading to the result VICARS
Buddy explains!

The straight part
We know that "Ministers" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ministers = vicars.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 VICARS mean?
VICARS noun- In the Church of England, the priest of a parish, receiving a salary or stipend but not tithes.
- In the Roman Catholic and some other churches, a cleric acting as local representative of a higher ranking member of the clergy.
- A person acting on behalf of, or representing, another person.