The most common and most likely answer to this crossword clue is the 3 plus 4 plus 2 plus 4 letter word THE SIGN OF FOUR
I've seen this crossword clue in The Daily Telegraph
T
H
E
S
I
G
N
O
F
F
O
U
R
More clues leading to the result THE SIGN OF FOUR
Buddy explains!
The straight part
We know that "detective story" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case detective story = the sign of four.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.