The Primal Style is a crafting skill that can only be learned by reading the book Crafting Motif 13: Primal Style. Crafting Primal items requires Argentum. Like all styles, it is purely cosmetic. Items will have the same stats regardless of the style you use. It was available in the Crown Store from April 13, 2015 to August 14, 2017, and remains available as part of the Crown Crafting Motifs Pack: Rare Styles bundle.
Primal items have fewer different designs than the ten normal racial designs (but still more variation than e.g. Ancient Elf Style). The Primal style progression seems to follow this pattern:
All armor has a single style across all material tiers.
All weapons and the shield have three different styles:
One style shared for Iron and Steel as well as Maple and Oak.