The most common and most likely answer to this crossword clue is the 8 letter word ORDINAND
I've seen this crossword clue in The Times
O
R
D
I
N
A
N
D
More clues leading to the result ORDINAND
Buddy explains!

The straight part
We know that "would-be priest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case would-be priest = ordinand.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 ORDINAND mean?
ORDINAND noun- A candidate for ordination