Destiny: Rising Exotics can be obtained by completing High-Value Bounties and receiving the Exotic Weapon Parameter currency. This currency can then be synthesized into a random Exotic from a specific activity, such as Strikes and Gauntlet Blitz. You can also earn Exotics by completing activities while having the Pinnacle Rewards currency available. Here is a breakdown of how to obtain Exotic guns.
High Value Bounties
These are your daily missions, requiring you to either get kills with a certain element or complete certain combat feats. The Exotic Weapon parameter currency is gained through the reward track, and completing all missions grants you 10 weapon parameters. The Strikes, Gauntlet Blitz, and Adventure exotic engram focusing costs 30 parameters, while the standard focusing costs 40 parameters.
Shifting Gates
This Gambit-like activity features a distinct reward tier, where reaching level 7 Research Rewards has a 0.33% chance to reward you with an Exotic engram upon completion. You can also obtain a random level 60 Mythic weapon when reaching this tier.
Haven Ops
This activity has a slightly higher chance of an Exotic drop, at 1% for every mission cleared. This will require the Pinnacle Reward currency to receive an Exotic drop.
Gauntlet Onslaught
This is a raid activity that offers the highest chance of dropping an Exotic weapon, with a 15% drop rate. However, you will need to be at 39600 Power to be on level with any of the encounters, and you will need a pre-made team to communicate for certain mechanics.
14 Day Sign-In Exotic Rewards
After logging in for 7 days and 14 days, you are rewarded with a guaranteed Exotic with a choice of either Huckleberry, Borealis, or Crimson as your free Exotic.