Silent Hunter is a gear perk that makes you quieter for a while after a bow kill. It keeps a bow user hidden while moving between targets in an outpost or on a hunt.
After you kill something with a bow, your movement makes less noise for a short time. That gives you a window to reposition without being heard.
Wear one of the listed boots or shoes. Gear perks are fixed to the piece of clothing that carries them, so you get this one by wearing that piece, not by unlocking it in a menu.
Big Quiver and Patient Archer support bow play, and Quiet Confidence does the same job for takedowns.