Summerset includes two new crafting motifs, while the previous DLC Dragon Bones also has two motifs available. Here is how to obtain the chapters and style items:
Renegade Dragon Priest
Complete the Scalecaller Peak Dungeon. It’s outside Summerset, but you need this DLC to be able to obtain this motif. This style of motif drops very rarely on Normal difficulty, somewhat rarely on Veteran, and always on Veteran hard mode.
Fang Lair
Complete the Fang Lair Dungeon. It’s outside Summerset, but you need the Summerset DLC to be able to obtain this motif. This style of motif drops very rarely on Normal difficulty, somewhat rarely on Veteran, and always on Veteran hard mode.
Psijic Order
The chapters and style item of this motif will drop from completing a wide variety of activities in Summerset: These activities include completing Abyssal Geysers and the smaller mini-geysers that occasionally pop up along the coastal areas, killing group bosses, killing delve bosses, opening treasure chests (random), and killing monsters throughout Summerset.
Pyandonean
Find the Pyandonean motif by fishing up Pyandonean Bottles, which you can do only in Summerset—not in Artaeum or any other zone. They replace the traditional gunny sacks that you can find by fishing in other areas. When you open a Pyandonean Bottle, you’ll always obtain a smattering of crafting materials, as well as either a chapter of the Pyandonean motif (or rarely, the full book) or a Sea Serpent Hide, the style item used in crafting Pyandonean-styled gear.
Sapiarch
Both the Sapiarch motif chapters and its style item come from completing the Daily Quests found in Summerset.