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While you're exploring different planets or ships in Starfield, you'll commonly find many useful items and place them in your inventory. You'll have very little inventory space in the game and will have to commonly look for vendors to sell away your valuable items and make a ton of Credits.
Some of these items can also include Contraband, which is illegal in almost every city. Most vendors in these cities won't accept your Contraband, and that's where the Trade Authority comes into play. You might have a hard time locating this Faction, and here are a few tips to help with that.
New Atlantis Trade Authority Location
New Atlantis is one of the first major cities you'll visit during the main story of Starfield, and it's located on the Jemison planet. You'll find the Trade Authority Kiosk on the right as soon as you land on the planet. You can use this to sell your items directly to the Authority, but it only has 5,000 Vendor Credits that regenerate slowly.
Keep in mind that you won't be able to sell Contraband items on these Kiosks. For that, you'll need to find the vendors directly.
To find the Trade Authority vendor in New Atlantis, head straight down the slope from your landing area and then turn left to find Jemison Mercantile. On the right of this shop, you'll see an elevator that'll lead you to The Well area. Keep going straight in this area and you'll eventually see a path leading to your left, which shows Trade Authority in front.
The Den Trade Authority Location
The Den is one of the best places to look for the Trade Authority since this area isn't covered with UC Vanguard or Freestar Collective ships. When you get close to The Den, you won't be scanned for Contraband unlike every other major city, which makes it one of the ideal places to sell your illegal items.
You can find The Den in the Wolf solar system on the top right side of Alpha Centauri. Get close and dock on the Staryard to be able to board it. Once you've boarded The Den, you'll find the Trade Authority Kiosk right in front. Moreover, you can find the vendor on the left after going straight from the spawn.
Neon Trade Authority Location
Neon is a bright city found on the Volii Alpha planet, and it's known for housing the Ryujin Industries. As soon as you land in the city, you'll find a building on your left that houses the Trade Authority Kiosk and the Ship Service Technician. To find the Vendor, you can take the path straight, which eventually leads to an elevator.
This elevator takes you to the main city where you'll find the Trade Authority building to your left on the front side. This is hard to miss due to the bright yellow-colored board.
Akila City Trade Authority Location
Akila City is one of the poor cities in Starfield, and it's also a place where the Trade Authority is quite hard to locate. Once you land in the city, head through the 'Welcome to Akila City' board and you'll find the Trade Authority Kiosk on the right side just before entering the city through the main doors.
However, the process to get to the vendor is a little more complicated. Enter the city through the main door and keep going straight until you see Galbank on your right. This is the same area where your first quest to get recruited by the Freestar Collective starts. Go up to Galbank and you'll see a path going to the right.
Follow this path and you'll find a giant dusty board with Trade Authority written on it.
Cydonia Trade Authority Location
Cydonia is a colony set up by the UC Vanguard in the SOL system, and it can be found on the top left side of Alpha Centauri. You can find the Trade Authority Kiosk on your left as soon as you land, right in front of the Ship Service shop. Cydonia is one of the few cities where you'll have to wear a Spacesuit until you get into the city.
If you want to find the Trade Authority vendor here, enter the main city and keep going straight until it opens up a bit. As soon as that happens, the Trade Authority shop will be on your right with a small white shining board on top. Other than all these locations, you can still find Trade Authority Kiosks in smaller cities like Hopetown.