Aside from permanently available adventures, you will also see temporary ones pop up in the game from time to time. When there is one, you will see a notification upon entering the game. It will show you the name and a short description of the adventure, how much time you have to complete it and the main reward.
You can travel to a temporary island by tapping its icon in the bottom right corner of the map screen or on the left side of the game screen below the notebook icon.
Once you get there, you will receive a mission. Complete all available missions in time, and you will get a unique and valuable reward. Make sure to explore too - temporary islands are abound in treasure!
And remember to claim gifts attached to in-game news posts announcing the appearance of temporary adventures!
Note: the start and end times of temporary adventures are fixed and are the same for all players.