The most common and most likely answer to this crossword clue is the 7 letter word SHOPPED
I've seen this crossword clue in The Guardian
S
H
O
P
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More clues leading to the result SHOPPED
Buddy explains!

The straight part
We know that "betrayed to the police" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case betrayed to the police = shopped.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 SHOPPED mean?
SHOPPED verb- To visit stores or shops to browse or explore merchandise, especially with the intention of buying such merchandise.
- To purchase products from (a range or catalogue, etc.).
- To report the criminal activities or whereabouts of someone to an authority.
- To imprison.
- To photoshop; to digitally edit a picture or photograph.