If you're tired of the the Drifter's questionably legal dealings, you'll want to follow the Destiny 2 Vanguard Allegiance quest. This is part of the pair of quest lines introduced in the Joker's Wild DLC, and if you take the Vanguard half, you'll oppose the Drifter and side with the Vanguard. This will affect how the Drifter treats you, but it won't impact your Gambit rewards or anything, so just follow your conscience. The quest is pretty similar no matter side you pick, but you can repeat it from a different perspective on another character to get the full experience.
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How to start the Destiny 2 Vanguard Allegiance quest
After you clear the short starter quest for Gambit Prime and The Reckoning, the Drifter will offer you a choice: stand with the Vanguard or stand with him. If you choose Vanguard, the Drifter will disavow you as a "snitch" and you'll be contacted by Aunor, the Warlock who's been sending you messages via the Postmaster. The first step of the Destiny 2 Vanguard Allegiance quest is to send a message of your own, so head to the hangar in the far right of the Tower.
When you reach the hangar, take the first right and look for a terminal underneath some stairs. Follow the GIF above if you can't find it. You'll return to this terminal several times throughout the quest, so commit it to memory. Compose your message, turn around, and poke around behind the Dead Orbit crowd until you find a messenger who'll carry your message. Here's another GIF if you can't find the messenger:
After receiving your message, Aunor will tell you to plant some bugs in the Drifter's home in the Tower. Fast-travel back to the leftmost landing zone and head into the hallway before the Drifter's room. You can plant all three bugs in the same spot, like so:
Next, Aunor will tell you to intercept a deal between the Drifter and Spider, the Fallen merchant in the Tangled Shore. Go talk to Spider and he'll request a hefty bribe of 50,000 Glimmer. Luckily, you can convert Legendary shards into Glimmer via Spider's inventory if you're running low. With that out of the way, it's time for some more action-packed quest steps.
Complete the Siren Song Adventure
Head to Titan and look for a special Adventure on the map. It's a 650 Power version of the Siren Song Adventure, but apart from some biting commentary from the Drifter, it doesn't play any differently from the normal version. Just follow the Hive and you'll be finished in no time.
Bank 50 motes in Gambit
This quest is all about monitoring the Drifter, so of course you're going to stop by Gambit. Luckily, you just need to collect and deposit 50 motes. You don't have to do it in one game, and you can run Gambit or Gambit Prime. I recommend Gambit Prime since the enemies there drop more motes, but you can play whatever mode you're comfortable with. In any case, it should only take you a round or two to bank 50 motes.
Get 25 kills in the Crucible
Crucible is next on the docket. Put on your best guns and head into whatever playlist you fancy. It doesn't matter how you get your kills - and yes, assists count - just that you get 25. So, channel your inner Shaxx and start shooting.
Visit the Derelict and find the Drifter's first hidden message
You'll need to visit the terminal in the Tower hangar after you polish off your Crucible kills, and then it's time to visit the Drifter's ship, the Derelict. Look for a special icon labeled "Mystery and Potential" on the Gambit activity director, just below The Reckoning, and head to the Derelict. Take a right as soon as you load in and follow the tripmine-lined hall until you reach the Drifter's, uh, lair. Scan the area and you'll find a hidden message from the Drifter.
Drifter hidden message locations
This is the first of eight messages. The rest are hidden around the EDZ. The locations for the other seven messages are the same no matter what half of the Allegiance quest you choose, so if you've already done the Drifter's quest on another character, you know where to go. If you haven't gotten the messages yet, here's where to find all seven:
Trostland hidden message:
Look for a group of Fallen pikemen and shanks near the Trostland landing zone. Head into the building nearby and look for a terminal on the right.
Skydock 4 hidden message:
This Lost Sector is inside the Cabal ship in the Sunken Isles. Take your sparrow under the ship, drop down the main tunnel in the back, and follow the right wall as you move toward the boss room at the end of the Lost Sector. The terminal is near the front of the room.
Flooded Chasm hidden message:
From the Gulch landing zone, hug the right wall and enter the first Lost Sector you come to. Inside you'll find a large chamber filled with Cabal and Fallen. There's a terminal near the middle of the battlefield.
Soujourner's Camp hidden message:
The Soujourner's Camp is on the way to the Bergusia Forge from the Black Armory, if that helps. Take the bridge at the south of the Outskirts and keep going until you reach the camp. Look for a tent on the right side; there's a terminal underneath.
Excavation Site 12 hidden message:
Look for the rightmost Lost Sector in Firebase Hades. Follow the linear path until you see the loot chest at the end. The terminal is behind the machinery next to the chest.
Winding Cove hidden message:
This terminal is right in front of the Winding Cove landing zone.
Scavenger's Den hidden message:
Head to the Outskirts and look for a sewer on the right side. Head inside, take the first right, and keep moving until you reach a cave full of Fallen. There's a terminal on the ground near a large purple tarp.
Confront the Drifter
Once you find all eight messages, speak to the Drifter in the Tower to complete the quest. You'll receive a reward from Aunor, who will dismiss the Drifter as an immediate threat - for now. As a bonus for siding with the Vanguard, you'll receive a bundle of loot every week, including an Enhancement Core and a piece of Powerful Vanguard gear. For this reason, I'll probably run the Vanguard quest twice and the Drifter's quest once, because lord knows I will do anything for enhancement cores.