The most common and most likely answer to this crossword clue is the 7 letter word CHECKER
I've seen this crossword clue in The Times
C
H
E
C
K
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R
More clues leading to the result CHECKER
Buddy explains!

The straight part
We know that "Person investigating" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case person investigating = checker.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 CHECKER mean?
CHECKER noun- One who checks or verifies something.
- One who makes a check mark.
- The clerk who tallies cost of purchases and accepts payment.
- One who hinders or stops something.
- A playing piece in the game of checkers (British: draughts).
- A pattern of alternating colours as on a chessboard.
- To mark in a pattern of alternating light and dark positions, like a checkerboard.
- To develop markings in a pattern of alternating light and dark positions, like a checkerboard.
- The fruit of the wild service tree or chequer tree, Photinia villosa, syn. Sorbus terminalis