Fan Missions can be found by clicking on the "Fandom" button on the Sessions main menu, and are a good opportunity for you to automatically grant Stars to the Artists that you're currently subscribed to.
The Fan Missions are weekly, and they will always reset on Sundays at 00:00 Pacific Time. Try your best to complete them as soon as possible to avoid having them expiring before you can complete them. You'll receive new Missions once they reset.