The most common and most likely answer to this crossword clue is the 4 letter word RUDE
I've seen this crossword clue in The Times
R
U
D
E
More clues leading to the result RUDE
- Impolite and cross, by the sound of it
- Bad-mannered prig head got rid of
- Rough diamonds in Parisian street
- Regret accommodating daughter that’s insolent
- Vulgar puritan is beheaded
- Regret about daughter having no manners?
- Rough rugby side? Not the first half
- Some of the durian rejected — like a raspberry?
- Insulting for a girl? Not half
- Verbally cross and discourteous
Buddy explains!

The straight part
We know that "Impolite" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case impolite = rude.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 RUDE mean?
RUDE adjective- Bad-mannered.
- Somewhat obscene, pornographic, offensive.
- Tough, robust.
- Undeveloped, unskilled, basic.
- Hearty, vigorous; found particularly in the phrase rude health.