One of the most highly anticipated additions the Isle of Armor DLC brings to Pokémon Sword and Shield is the new cosmetic options. However, downloading the DLC alone will not automatically give you the new options. To unlock them, you need to get the Style Card.
How to get the Style Card
When you arrive at the Isle of Armor and exit the train station, a senior dojo trainer will challenge you to a battle. In Pokémon Shield, you will face off again Psychic-type trainer Avery, and in Pokémon Sword, you will face off against Poison-type trainer Klara.
If you defeat them, they will gift you the Style Card.
How to use the Style Card
The Style Card will add more options to both the boutiques as well as the salon back on the mainland. The first time you arrive with the Style Card, the sales clerk will comment on how there will be new options added: New clothing at the boutiques and new hairstyles at the salon.
All new options will be indicated by a rectangle covered in sparkles, indicating that the option is only available because you have the Style Card. Be wary though: you cannot wear hats with the new hairstyles.