Exotic items are orange tier (tier 4) items. They can be received from loot or be randomly crafted from the craft menu at the keep.
The quickest way to acquire better loot is through quickplay, which adds an additional multiplier to loot received at the end of the mission.
Additionally, completing challenges and quests using Okri's Challenges in the fort can also provide you with a steady stream of additional loot; thereby increasing your chances of getting better gear.