The most common and most likely answer to this crossword clue is the 8 letter word SEMINARY
I've seen this crossword clue in The Sunday Telegraph
S
E
M
I
N
A
R
Y
More clues leading to the result SEMINARY
- House not ever needed as college
- College not halved?
- Changed in 1000 years
- Marines trained for a year in academy
- Is my religious education an outcome of this place?
- Theological establishment, house no rector would enter
- Religious establishment never follows House
- Where ministers could have learnt from poor miner, say
- College remains crumbling close to Ely
- Many rise when trained in educational establishment
Buddy explains!

The straight part
We know that "Where ministers could have learnt" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case where ministers could have learnt = seminary.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 SEMINARY mean?
SEMINARY 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.
- Of or relating to seed; seminal.