The most common and most likely answer to this crossword clue is the 5 letter word SNOOP
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More clues leading to the result SNOOP
Buddy explains!

The straight part
We know that "Detective" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case detective = snoop.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 SNOOP mean?
SNOOP noun- The act of snooping
- One who snoops
- A private detective
- To be devious and cunning so as not to be seen.
- To secretly spy on or investigate, especially into the private personal life of others.