Spoiler Free

• Seasons are 91 days long so Season of the Drifter ends June 4th
• There's an Exotic Kinetic in the database listed as Classified. (Right next to Thorn and Arbalest, so it's not those)
• /u/Ginsor Posted all the UI Images for the latest patch and no new weapon icon has been found.
• Tess has TWO (1, 2) persistent packages for sale, code named commando. These are likely to be skins for the weapon. Looks like these skins are attacked to an unknown Energy Weapon... wat?

Speculation

Date

We probably won't see the quest until May. Revelry ends on May 7th. On May 14th players will be able to visit Mara for the "last" time and collect the full Truth to Power lore book, and a few days before on May 10th we will receive the ninth invitation from Xur. There's a strong chance this might lead into the free exotic questline and the next season.

Weapon

So far, these quest lines have been used to bring back existing exotics from Destiny 1 into the Destiny 2 universe. From that we can speculate which weapon it might be, assuming they continue the same pattern. The following list are all Destiny 1 Exotic weapons in the Kinetic slot (I excluded raid exotics as they seem the least likely to make a return):

• Bad Juju (I think this is the most likely)
• Monte Carlo
• No Land Beyond
• Universal Remote
• Boolean Gemini
• The First Curse
• Khvostov 7G-0X
• Tlaloc
• Red Death (Unlikely, as we already have Crimson)
• Zhalo Supercell (Unlikely, as we already have Riskrunner)
• Fate of all Fools (Unlikely, as we already have Jade Rabbit)
• Hawkmoon (Unlikely, Rumored to be next season)
• Fabian Strategy

There's also two unknown Exotics from the first game

• Devils' Due (This is the one I want to see, because of it's lore)
• Punk Prayer

Unrelated Item

There is a new item in the database called Lost History. It reads: Whispers from events in the past, triumphantly retold and added to your Guardian's legend.

This sounds more like an item to connect PS4/XB1 and PC accounts for all of the Destiny 1 Triumphs (like doing the raids). Note: Just because it's in the database doesn't always mean it will make its way into the game (see Devil's Due and Punk Prayer above).

Perks

This are also new Traits. The first is called Once More that reads: Reloading increases this weapon's damage if you hit with at least half the rounds in the magazine, but fail to kill anything.

The second is Hailstorm. This reads: Kills increase this weapon's damage and begin to steadily reload the magazine from reserves until you stop firing.

It's possible the new weapon can have both of these, or none of these. The Hailstorm perk looks to be a rework of the Bad Juju perk "String of Curses": After each kill, this weapon will reload instantly and increase damage for a short time. Kills will help charge your super.

Spoilers

Inside of /u/Ginsor's post linked above there is a new mission string: Zero Hour (Heroic). There is also a description: Thwart a heist alongside a new ally. This is most likely part of the free quest line. So who is this new ally? I think the obvious first choice is Uldren Sov. We haven't seen him since he was revived by Pulled Pork. It's also pretty close to the final time we'll go to the Queen's Court.

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Updates

I added a few missing Exotic Kinetics from Destiny 1 and /u/DasGuppy pointed something out to me. The two Tess packages are NOT connected to an Exotic Kinetic weapon but are instead connected to an Energy Weapon. The only other persistent package with a code name is Whisper (candycane) so it's likely an Exotic Energy Weapon.

So that means either: Something is mislabeled (the Gun is Energy and not Primary and this post is useless, or the packages are wrong), or there are TWO exotic weapons on the horizon (one from quest, one hidden like Whisper).

I troll around in the database quite a lot and I'm more inclined to say it's the first and that something is mislabeled. But something to think about...