As noted in the announcement for Mafia III: Definitive Edition, that version of the game comes with all its associated story downloadable content. If you already own the original Mafia III on consoles then you don't need to purchase the Mafia III: Definitive Edition to enjoy the game's DLC: It's now available for free.
If you own the game on PC, the DLC should be automatically enabled. However, if you're in the PlayStation or Xbox store, search for the “Mafia III: DLC Content Pack." Once you've selected it, you should be able to download it for free.