The most common and most likely answer to this crossword clue is the 11 letter word FINGERPRINT
I've seen this crossword clue in The Guardian
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Buddy explains!
The straight part
We know that "Personal impression gathered by the police" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case personal impression gathered by the police = fingerprint.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 FINGERPRINT mean?
FINGERPRINT noun- The natural pattern of ridges on the tips of human fingers, unique to each individual.
- The patterns left on surfaces where uncovered fingertips have touched, especially as used to identify the person who touched the surface.
- Unique identification for public key in asymmetric cryptosystem.
- A unique combination of features that serves as an identification of something.
- A trace that gives evidence of someone's involvement.
- To take somebody's fingerprints.
- To identify something uniquely by a combination of measurements.