After the dramatic events in Galar and the Champion Cup, you continue your adventure in Galar.
Get a Master Ball
Leave your room and there will be a cutscene. You will get a Master Ball. It is guaranteed to catch any pokémon, so be sure to save it for a special pokémon.
Visit the Shrine in the Slumbering Weald
If you go into the Slumbering Weald and go northwest each time the path splits, you will find the shrine again. This is where you can begin the main post-game quest.
Get a Charmander
Go into Hop and Leon's house and go upstairs. Go east and check on the pokéball to get a Charmander.
Visit the Battle Tower
Rose Tower is now the Battle Tower, where you can battle trainers to earn BP and win items. There is a TM shop with rare (and expensive TMs), and there are BP shops where you can buy mints for changing pokémon natures, and other rare items.
Get a Type: Null
In the Battle Tower, talk to the League Staff member who is standing next to a Type: Null to receive the Type: Null and all of the memory discs that its evolved form can use.
Learn Steel Beam
Go to the western Pokémon Center in Motostoke, then go east until you see the large door with the Lapras logo on it. Go south from there, and follow the path to the end. You can talk to the person there to teach your pokémon Steel Beam.
Get the Oval Charm
Go into the west building of the Hotel Ionia and go up the elevator. Go into the first room to the left of the elevator and talk to the police officer. You will have a double battle with GAME FREAK's Morimoto, who has a level 65 Cursola, a level 65 Grapploct, a level 65 Stonjourner, a level 65 Dragapult, a level 65 Coalossal, and a level 65 Snorlax that he will Dynamax on the first turn. If you win, you get 13000 Pokédollars, and you get the Oval Charm. It makes eggs appear sooner when you leave two compatible pokémon in the Nursery.
Get a Beast Ball
In Stow-on-Side, talk to the person who sells bargains (between the Maractus and the rare item buyer) to get a Beast Ball. It works best on Ultra Beasts.
Get the Shiny Charm
If you have caught all 400 pokémon in the Galar pokédex, you can go into the western building of the Hotel Ionia in Circhester, go up the elevator, and go into the first room to the left of the elevator, and talk to the doctor to get a Shiny Charm, which increases your chance of finding shiny pokémon.