The most common and most likely answer to this crossword clue is the 9 letter word DOCTRINAL
I've seen this crossword clue in The Daily Telegraph
D
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More clues leading to the result DOCTRINAL
Buddy explains!

The straight part
We know that "of religious teaching" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case of religious teaching = doctrinal.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 DOCTRINAL mean?
DOCTRINAL noun- A matter of doctrine, or system of doctrines.
- Of, relating to, involving, belonging to or concerning a doctrine.
- Didactic.