Anthe would like a Red Shard, Green Shard, and Blue Shard to help with her fashion designs.
The Request
Talk to Anthe in Jubilife Village to accept this request.
Get Shards
Shards can appear in space-time distortions. Check for space-time distortions when you leave Jubilife Village. Wait inside a space-time distortion until it has finished forming. Shards and items and pokémon will appear at random. Go around and gather shards until you have at least one red, one green, and one blue shard.
Reward
Give the shards to Anthe in Jubilife Village and she will add new items to her lineup.