To store weapons in Days Gone, you must first purchase a weapon from a merchant. Once purchased, you can then store it in a weapons locker in an encampment.
Any weapons you purchase will also be available through the Encampments Weapon Locker – this also includes pre-order bonuses and DLC weapons.
You also cannot store the weapons that you can find in the game. It's a real shame because you often find better ones than the ones sold.
Related: Days Gone: All Nero Checkpoint Locations
So if you want to store or keep these weapons you will have to keep them on you because if you drop them they will be gone forever.
However, you can unlock better ones by completing various missions and earning the trust of survivor camps. You can also gain trust by doing the following.
- Hunt down the freakers and turn their ears at the Bounties station
- Donate items to the kitchen
- Complete Main Story Missions
- Complete Bounties, Needy Campers, and Supply Runs
When you get high enough confidence, you can get better weapons, among a ton of other items and upgrades for your guns and motorcycle.
For more on Days Gone, we recommend checking out both How to Fix the Black Screen Bug in Days Gone and Horde Locations in Days Gone.