In Days Gone you have a Weapon Locker. But you may have noticed that weapons dropped by enemies cannot be stored in that weapon locker.
So how to unlock new weapons?: Simply buy them.
Only weapons you have bought from camp merchants get added to your locker. The ones you find from enemies cannot be stored anywhere and will be left behind when picking up another weapon instead. So only the weapons you have bought are permanently available.
What can be a bit confusing is that the first camp “Copeland’s Camp” doesn’t sell any weapons at all. The second camp you reach called “Hot Springs” in Belknap region is the first one with a weapons vendor. The more trust you have with a camp the more weapons will be available. Weapons also cost money and every camp uses its own currency that cannot be spent at other camps.
You gain trust and money from Story Missions, Encampment Jobs, Hordes, Nero Checkpoints, Ambush Camps, Infestations, Survivors and Bounties.