You can check the remaining time for your active Adventure on the scroll icon under your character portrait in the upper-left part of the screen. Tap on the scroll icon and select the Side Quests tab - the time left is also shown under the title of the Adventure.

TIP: You can extend the duration of your Special Adventure by tapping on the clock icon next to its title. This will allow you to spend 55 gems or an add-time toffee to extend your quest by 3 hours or watch a video ad to extend it by 20 minutes.