This guide will tell you where to find your DLC in Wild Hearts.
You will need to progress until you get your first camp and then go to the blacksmith. Build the blacksmithing thing, and then you can start changing your equipment. The empty slot is basically for cosmetics.
But it will not give you any actual armour. Your DLC armour will be in any of these spots there. If you are looking for Chat DLC, press Start to go to chat, and your stamps will be over there. You can assign them to a shortcut; emails will be over there. Just click them and assign them what you want to do.