The short-short answer: Bessel star system -> Planet Bessel 3 -> Abandoned Muybridge Pharmaceuticals Lab -> In the lower of the three structures -> In a backroom directly above the cave entrance -> In the lockers.
Or...
If you're like me, you loved the UC Security uniform the moment you saw it. One would think completing the UCSEC questline would award you with your very own freshly minted set of security armour, along with the unique and beautiful helmet that comes with it. Or perhaps it would be purchasable from the UC Distribution centre in the mercantile district, given that is the distribution centres' exact purpose. No such luck I'm afraid.
Also like me, you may now be desperately searching for the full suit of armour for yourself, your crew and your companions. Well, finding multiple sets is completely doable, even if it's not obvious how. Allow me to help.
Apparel, not armour.
The first thing to know before you go barreling off into space is that the UCSEC armour isn't actually armour, it's apparel, and so is the helmet. I found this disappointing as it looks as though it should be a full-fledged spacesuit. The benefit though is that you can wear both underneath your chosen spacesuit and helmet and they have pretty decent stats.
And in case you weren't aware, because I certainly wasn't for an embarrassingly long amount of time, is that starfield has a built-in option to autohide your armour and helmet when you're in a friendly settlement. Open your inventory and navigate to your spacesuits and you'll find the option there. This is the best of all worlds as you'll be able to rock the UC rep across the settled systems, whilst still benefitting from all your kits' full stats.
Leave a friendly settlement and your primary armour (spacesuit/helmet) will re-appear seamlessly. Thanks Bethesda!
The locations.
So first off, the UCSEC armour can be found right in New Atlantis. Head over to Jemison Mercantile next to the starport and follow the exterior of the store as it curves around to an understated alley area. In this little alley/side area will be a discretely placed elevator. Head inside and hit the button.
This will take you to a grubby underside of New Atlantis that should be burned down and rebuilt, known as The Well. The Well is also accessible through an elevator located in the Mast districts' travel terminal, but this will pop you out on the far side, not where we need to be.
Exiting the elevator directly next to Jemison Mercantile, you'll find yourself atop a short set of stairs with a full UC Security station to the left. Head inside, go to the back and open the door. Just past this door, you will find a series of lockers full of UCSEC uniforms. Close the door, enter sneak mode, and steal as many as you like. The UC takes care of its' own after all, and I'm sure the on-duty officers will be re-issued their uniforms without much fuss, especially if they all lose their uniforms at once in a security breach. This should also act as a nice wake-up call to increase security before a bad actor with hostile intent can do some serious damage. So don't let the theft keep you up at night and take those uniforms!
The only problem now is they're listed as stolen in your inventory, and will be confiscated if you're caught. To get around this, head straight out the front door, run until you pass the first corner, take a left, and you should be able to find your way to the local Trade Authority.
Sell the clerk your liberated uniforms, before swapping over to the buy-back tab and purchasing them. These are now legal and clear, yours to keep.
But what about the helmet?
A little bit of travel...
You would think the helmet would be located with the other outfits in the back of the UC Security station. Or liftable from their inventory with some simultaneously dextrous and sticky fingers. Perhaps even collectable after a fellow brave officer that has been gnawed on a little too hard by a surprise Terramorph, I've not encountered a single one in my attempts. So that means we need to hit the road.
Hop in your ship and take flight. You're looking for the Bessel star system, located north-north-west of Alpha Centauri and Sol.
Within the Bessel system, you're looking for Bessel 3 specifically.
Once you arrive in Bessel 3's orbit, scan the planet. You're trying to locate the Abandoned Muybridge Pharmaceuticals Lab in the northern hemisphere, very close to the north pole.
Break out your meanest, most painful, most war-crimeiest weapon as the three buildings are infested with House Va'ruun zealots. Exterminate them in the goreiest way possible. That's for The Den!
Once they're dealt with, head to the lower of the three buildings. Towards the back will be a secure door. Open the secure door and you'll immediately see a row of lockers. Open these lockers and you'll find another UC Security outfit along with the beautifully done UC Security helmet.
Alternatives.
This article was written on the 3rd of October 2023. Starfield is still a brand new game with lots of information missing and so much yet to be uncovered. It's almost guaranteed other locations will be discovered as we go, and hopefully sooner rather than later as currently there is only a finite number of outfits to share between you and your crew.
So far, the only other location I am aware of is described in this Reddit thread of a single set located in the Nova Glactic staryard, next to Luna in the Sol system.
Wrap up.
And with that, my fellow United Colonies citizen, you should have all the information required to procure your own sets of UCSEC and UC Security armour/outfits. Hold your head high as you represent the UC and the order, safety and quality of life it brings to the people of the settled systems.
I'll see you out there amongst the stars.