An update for Pokemon Sword and Shield was released on January 9, 2020 after the Pokemon Direct, which revealed the Pokemon Sword and Shield expansion pass.
Even if you haven’t purchased the expansion pass, you can still get a Galarian Slowpoke.
Once the update is live, connect to the internet at least once. Then head to Wedgehurst Station. It’s the first town in it with a train station in Pokemon Sword and Shield.
Once inside, you will meet a new trainer. In Pokemon Sword, you’ll encounter Klara; and in Pokemon Shield, you will encounter Avery. Then, you will be able to get a Galarian Slowpoke.
Finally, you will need to battle and catch Galarian Slowpoke to actually get it. It’s a Lvl. 12 Slowpoke but don’t worry if you cause it to faint. The only way to “stop the Slowpoke from blocking the turnstyle” is to catch it so worst case scenario you’ll just have to do the battle again. We recommend using a Quick Ball on the first turn. Other recommended Poke Balls include the Level Ball (Pokemon that are a lower level than your own are easier to catch) and the Turn Ball (more effective each turn).
How to Evolve Galarian Slowpoke
To evolve Galarian Slowpoke, you will need different special items.
To get a Galarian Slowbro, you will need an item from The Isle of Armor.
To get a Galarian Slowking, you will need an item from The Crown Tundra
It is unknown what these items are called or how to get them just yet.