Dragon Age: The Veilguard

If you head to the “Wardrobe” at the Lighthouse in The Veilguard (i.e. the gold chest in the Lighthouse when you first get there, or the wardrobe in the meditation room when you get access to that), you’ll be able to interact with the game’s transmogrification system, allowing you to change the look of a piece of gear without changing the stats.

To unlock the ‘A New Look’ achievement, then, you need to head there and quite simply change the look of any piece of gear for the first time. Once you do, this achievement is all yours.