I haven't completed the Definitive Edition yet so I can't say if these are made available in the main game as well. The first 2, Year of the Snake and Nightmare in North Point are both available from the main menu before you start the game. The icon for Zodiac Tournament will then appear on your map where it usually does and you will be able to proceed with playing it. For example, you will get a text from Inspector Teng at a certain point letting you know of an illegal fighting ring she found out about. The last 2, Zodiac Tournament and Wheels of Fury unlock as available missions as you play. Year of the Snake, Nightmare in North Point, Zodiac Tournament and Wheels of Fury. This means that almost all of the DLC needs to be unlocked in the game through game play and is not available from the start. Unlike the standard edition of Sleeping Dogs all of the DLC in the Definitive Edition has been made a part of the game.
Trust me, everything is there for the finding! :) That being said if you would like to find out about the DLC in the game on your own I would suggest you stop reading now and go explore Hong Kong. It is different than I have seen in a lot of games, especially the standard edition of Sleeping Dogs. I've seen some confusion on how the DLC works in the new Definitive Edition of the game and thought I would put something together to help avoid this. As quoted from StanceStrife on the official Sleeping Dogs forums:
