Partner Play

Play with Partner is a brand new feature introduced in Pokémon: Let's Go, Pikachu! and Let's Go, Eevee!. It is the successor of Pokémon-Amie and Pokémon Refresh.

Description
From Pokémon: Let's Go, Pikachu! and Let's Go, Eevee! official site:

In between exploring and battling, it’s a good idea to relax with your Pokémon buddies. Enjoy a little playtime with Pikachu or Eevee in order to strengthen your bond with it. It will sit on your arm, allowing you to pet, feed, and even tickle it. Good things might happen as the two of you become closer.

You can play with your partner Pikachu or Eevee when you’re not in battle by selecting the Pikachu or Eevee icon on your main menu. The more time you spend with your partner, the more it’ll grow to love you! As you become closer, it’ll give you high fives or even find gifts for you as you travel. Lots of good things can happen if you’re friends with your partner!

Interact with your partner Pokémon by controlling the cursor with a detached Joy-Con. You can pet and play with your partner, and it may even grow closer to you as you become friendlier with it. In handheld mode, you’ll be able to play with your partner directly by using the touch screen.