Joker obviously killed Gambol, but we never actually see how he did it, whether it was slicing the side of the crime boss’ mouth or slitting his throat.
Admittedly, we never actually see Gambol die in The Dark Knight.
But in the final cut, Gambol was quickly taken out, and Joker proceeded to hold “tryouts” for his newly-acquired gang.
In case you need a refresher, Heath Ledger’s Joker staged it so that some goons of his would deliver his body to Gambol’s hideout under the ruse that they’d killed the clown, only for Joker to rise up and hold a knife to Gambol’s mouth.