You can only have one Special Adventure active at a time. Once you complete your active quest, the next available one will start after a 24-hour cooldown (if you have multiple unlocked quests).

 TIP: If you have multiple Adventures in your quest queue that you would like to complete quickly, try taking a break from the main story tasks while you wait for them to start. The further you progress through the main storyline, the more new Adventures you unlock, which can increase the backlog of your available quests.