Sometimes you may feel that you need more workers on your island or have a task where you have to send a character that you don't have yet to do something. Usually, it means that there is a new Rescue Expedition available for you where you can find most of the permanent characters.

The Rescue Expeditions are located in the Map menu at the left bottom of the game. 
   

These expeditions are not time limited, so  you can finish them in your own pace. Besides, there you will also be able to find unique decorations, new pets, as well as stock up on important resources!