In Pokémon Sword and Shield, there are Galarian versions of Slowking and Slowbro. The item to evolve Slowpoke into Slowbro was available in the Isle of Armor expansion pack. The Galarian item for Slowking can only be found in Crown Tundra, so you need to have the expansion pack to obtain both of these Pokémon. We were able to discover the item you need to use to evolve it into Slowking.
You need to make your way across the map to the east section of the Crown Tundra location. You want to go all the way to the east, over by the Frigid Sea. Here it is on the Sword and Shield map.
The woman you want to speak to is to the left. Enter the water, and rather than go out into the open sea, go to the left, and you should find a small cave cut into the side of the mountain. Proceed to the cave, and there should be a woman to the right side that you can speak to, and she’s offering to make you a Galarcia Wreath.
The item you need is a Galarcia Wreath. To make the Wreath, the woman requires 15 Galacia Twigs that you have to find around the island. These twigs are a little difficult to come by. You can find them out in the wild area of Crown Tundra, and they’re the sparkling items you see on the ground. You’ll have to travel around the island to acquire enough of them, and when you have all 15, return to the woman.
After you have the wreath, provide it to your Slowpoke, and it should evolve into a Slowking. You don’t have to level it up. All you have to do is give it the item from your inventory.