The most common and most likely answer to this crossword clue is the 6 letter word SQUIRT
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More clues leading to the result SQUIRT
Buddy explains!

The straight part
We know that "Impudent person" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case impudent person = squirt.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 SQUIRT mean?
SQUIRT noun- An instrument from which a liquid is forcefully ejected in a small, quick stream.
- A small, quick stream; a jet.
- (hydrodynamics) The whole system of flow in the vicinity of a source.
- A burst of noise.
- An annoyingly pretentious person; a whippersnapper.
- A small child.
- Female ejaculate.
- (of a liquid) To be thrown out, or ejected, in a rapid stream, from a narrow orifice.
- (of a liquid) To cause to be ejected, in a rapid stream, from a narrow orifice.
- To hit with a rapid stream of liquid.
- To throw out or utter words rapidly; to prate.
- (of a female) To ejaculate.