There are many different ways to play Deathloop. This includes changing your perks, weapons, playstyle, and trinket loadout. One way to customize your playthrough that you might not have thought about is changing your outfit.
To unlock these outfits, you simply need to play as Julianna in multiplayer mode. Killing Colt while in this mode and leveling up will unlock outfits for both characters. This is the only way to unlock them as there are no microtransactions or in-game store to purchase them from.
You can unlock outfits and change both Colt and Julianna's look as you play. As outfits are only cosmetic, they will have no effect on your gameplay except for changing Colt and Julianna's appearance. This means that all of your perks and weapons will play the same no matter how your character looks. This doesn't mean you shouldn't worry about outfits though.
To change a character's outfit, select the Loadout option from the main menu. Select the character whose outfit you want to change and you will be given the option to Change Style. Select this option to view all the outfits you have unlocked so far. Simply navigate to the outfit you want Colt or Julianna to wear and select it.
For more information on Deathloop, check out How Does Progression Work in Deathloop? and What can you do with glowing objects in Deathloop? on Pro Game Guides.