The most common and most likely answer to this crossword clue is the 10 letter word IRREVERENT
I've seen this crossword clue in The Times
I
R
R
E
V
E
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N
T
More clues leading to the result IRREVERENT
- Disrespectful library oddly ignored event including monarch
- Impious bishop on island about to engage in affair
- Non-Western writer never turning against religion?
- Tail of golden retriever wags – that’s cheeky
- One bishop has little hesitation to get into affair that’s un-bishop-like!
- Irish torn about always being rude
- Godless hiding gun in disguised terrine
Buddy explains!

The straight part
We know that "Impious" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case impious = irreverent.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 IRREVERENT mean?
IRREVERENT adjective- Lacking respect; not having or not showing respect for or seriousness towards something that is usually treated with respect; going against conventional precepts.