After you defeat the Elite Four and watch the credits, press a button when it says The End, and new things will be unlocked!
Cerulean Cave
After the credits roll and you press a button when it says The End, go down the stairs. Your rival will come up and say that a strong pokémon was seen going into Cerulean Cave. Cerulean Cave is northwest of Cerulean City.
Fly in the Sky
When you leave your house after defeating the Elite Four, you see a message that says you can fly in the sky with Charizard, Aerodactyl, and Dragonite. Aerodactyl is the easiest to get if you don't already have one of those three flying pokémon. Just go to Pewter City, chop down the tree east of the Pewter Museum entrance, and go into the side office. Talk to someone there to get an Old Amber, then go to Cinnabar Island and go into the Pokémon Lab, and give the Old Amber to a scientist in the Experimental Lab room to turn it into Aerodactyl.
Flying lets you float above the land, moving freely above obstacles. You can't fly through gatehouses, but it is still much faster than walking.
You can also encounter wild pokémon while flying. You can encounter very rare pokémon while flying if you have a big catch combo going.
Master Trainers
Ronny from Route 1 tells you that Master Trainers have appeared throughout Kanto. If you are playing Let's Go Eevee, Ronny tells you that there is an Eevee Trainer or Pikachu Master that you can challenge in Pokémon Road (also known as Route 17). If you are playing Let's Go Pikachu, Ronny tells you that there is a Pikachu Trainer in Viridian Forest.
In a battle with a Master Trainer, you have to use the same species as the Master Trainer, and you can only use one. You can't use items during the battle.
A Master Trainer will have a speech bubble that shows the type of pokémon that the trainer will use.
Pokémon Trainer Red
After you defeat 6 Master Trainers, go to the Indigo Plateau and you can battle Red outside the building.
Rocket Admin Archer
You can battle Rocket Admin Archer in the Viridian City Gym, where you battled Giovanni before.
Jessie and James
After you defeat Archer in the Viridian City Gym, you can battle Jessie and James in Route 17. You will get new items for your Clothing Trunk after the battle.
Gym Leader Rematches
Go to the Pokémon Gyms throughout Kanto and you can have a rematch with the Gym Leaders once a day to get EXP and Pokédollars.