The most common and most likely answer to this crossword clue is the 10 letter word SEMINARIES
I've seen this crossword clue in The Guardian
S
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More clues leading to the result SEMINARIES
Buddy explains!
The straight part
We know that "Where potential ministers learn" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case where potential ministers learn = seminaries.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 SEMINARIES mean?
SEMINARIES noun- A theological school for the training of rabbis, priests, or ministers.
- A private residential school for girls.
- A class of religious education for youths ages 14–18 that accompanies normal secular education.
- A piece of ground where seed is sown for producing plants for transplantation.
- (by extension) The place or original stock from which anything is brought or produced.
- Seminal state or polity.
- A Roman Catholic priest educated in a foreign seminary; a seminarist.
- An academic seminar.