You travel through South Province (Area Two) to reach the Cortondo Gym, where you can challenge Bug-Type Gym Leader Katy.
Nemona will meet you in the lobby of the gym. She gives you 3 Super Potions.
Cortondo Gym Test
Talk to the person behind the front desk in the lobby of the Cortondo Gym.
Exit the gym and leave town by the west exit, then go north up the path to the fenced area. At the quest destination, talk to the person you find, who will explain the Olive Roll to you. If you are ready, say Yes.
You can ride Koraidon/Miraidon (or just walk) and roll the large olive-shaped ball along the path. When you reach the corner, you can optionally go north and talk to the trainer there to open a shortcut. This is Gym Trainer Esmeralda, who has a level 13 Kricketune. You get 1820 Pokédollars for winning.
Northwest of that trainer, there is another trainer that you can talk to for an optional battle that opens a shortcut. This is Gym Trainer Antonio, who has a level 13 Venonat. You get 1820 Pokédollars for winning.
The goal basket is in the middle of the north wall. You can use Koraidon/Miraidon to help you roll the olive into the goal basket. After it's in the basket, you will pass the Gym Test.
Go Back to the Gym
Go south from the Olive Roll and go east into the town, and go into the Cortondo Gym. Talk to the person behind the front desk. If you are ready, say Yes to challenge Gym Leader Katy.
Gym Leader Katy, the Sugarbug
Katy has a level 14 Nymble, a level 14 Tarountula, and a level 15 Teddiursa that she Terastallizes. Its Tera type is Bug. You get 2700 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 TM021 Pounce.
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.