During the Moonlight Seeker event, you will need to find the Mystmoon chests and Moonchase charms, which are scattered around the map. Completing these missions will bring you rewards like primogems, mora and fish claymore.
To participate in the Event, you must have an Adventure Rating of 28 or higher and have completed the ‘A New Star Approaches’ and ‘Mondstadt Gastronomy Trip’.