Saturday's Client — that's labyrinthine detective story (1,5,2,7)
I believe the answer is:
a study in scarlet
'detective story' is the definition.
(Sherlock Holmes novel)
'saturday's client that's labyrinthine' is the wordplay.
'that's labyrinthine' is an anagram indicator (labyrinthine can mean complex or convoluted).
'saturdays'+'client'='saturdaysclient'
'saturdaysclient' anagrammed gives 'A STUDY IN SCARLET'.
(Other definitions for a study in scarlet that I've seen before include "colourful interior decoration for scholar?" , "Work" , "novel" , "mystery" , "Book" .)