After you explore the big city of Levincia, you enter the Levincia Gym for the Gym Test.

Enter the Gym
When you enter the Levinia Gym, there will be a cutscene, and Nemona challenges you to a battle. She has a level 21 Rockruff, a level 21 Pawmi, and a level 22 starter pokémon that she will Terastallize (Quaxwell if you chose Sprigatito, Floragato if you chose Fuecoco, Crocalor if you chose Quaxly). You get 1320 Pokédollars for winning.
Afterward, Nemona gives you 3 Full Heals. Your Pokémon have been healed up, and your Tera Orb has been recharged.
Levincia Gym Test
If you're ready, talk to the person behind the counter in the Levincia Gym, then go outside, and there will be a cutscene.
The challenge is a game of hide-and-seek with Director Clavell. You will have to find him three times.
When the challenge begins, move the magnifying glass over Director Clavell. He is on the right side of the screen, sitting at the table on the left.
Next, you will battle Gym Trainer Marti, who has a level 22 Luxio. You get 3080 Pokédollars for winning.
After that, you need to find Director Clavell again. He is on the left side of the screen, behind the counter of the Pokémon Center, in the place where the person who heals your Pokémon usually is.
Next, you will battle Gym Trainer Michael, who has a level 22 Tynamo and a level 22 Flaaffy. You get 3080 Pokédollars for winning.
Then you have to find Director Clavell one more time. He is on the right side of the screen, in a boat down below the battle area.
Electric Gym Leader, Iono, the Supercharged Streamer
Heal up at a Pokémon Center, then go back to the Levincia Gym and talk to the person behind the counter. If you are ready to battle Iono, say Yes.
Iono has a level 23 Wattrel, a level 23 Luxio, a level 23 Bellibolt, and a level 24 Mismagius that Iono Terastallizes, with Tera Type Electric. Mismagius is immune to Ground attacks because of its Levitate ability. You get 4320 Pokédollars for winning.
You will get a Gym Badge. Check the Gym Badge Effects page to see the level of Pokémon that will listen to you and be easier to catch, or open the Map App or Pokédex App and press X, then select Profile, then press A to see the effects of your current badges.
You also get a TM048 Volt Switch.
New Sandwiches
A new Gym Badge means new sandwich recipes. Be sure to stop by any Every Wich Way and talk to the person in front of the counter to learn some new recipes.