After visiting Professor Kukui's lab and the Pokémon Center, your next stop is the Trainers' School.
Go to Trainers' School
When you're ready to continue, go outside and go to the left to reach the Trainers' School. You'll notice that a Tauros is blocking the path to the west.
In the school, go up to Lillie and the others. Professor Kukui gives you the Exp. Share. If you turn it on in your inventory, all of your pokémon will receive experience after a battle, even if they didn't participate in the battle. The Exp. Share is turned on by default.
Defeat the First Trainer
You need to find the four trainers in the school and defeat them before you can continue. You can talk to Lillie if you need to be healed up.
In front of the bottom-right corner of the building, there is a Potion.
If you go northeast from there and talk to the girl, you will fight one of the four trainers: Youth Athlete Hiromi. She has a level 7 Bonsly. You get 196 Pokédollars for winning.
Defeat the Second Trainer
Go southwest from there. There is a Potion between the trees in front of the school. South of that, you find a pokémon battling area. The boy in this area claims to be the strongest, and won't battle you until you have defeated the others.
Now go northwest until you find a red gate in the fence to the left. Check on the gate to open it.
Go south and you can find an Antidote southwest of the first patch of grass. Farther south, there is a Paralyze Heal on the left.
Go south and talk to the boy there. He is another of the four trainers: Youngster Joey. He has a level 7 Grimer. You get 140 Pokédollars for winning.
Defeat the Third Trainer
Now go into the school. Go to the east side of the ground floor. Talk to the girl in the white dress to get a Quick Claw.
Go to the west side of the ground floor and enter the classroom. Talk to the girl in the upper left of the room. She is Preschooler Mia and she has a level 7 Metapod. You get 84 Pokédollars for winning. She also gives you three Oran Berries.
Defeat the Fourth Trainer
Now go back outside and talk to the boy in the green clothes who is standing in the pokémon battling area. He is Rising Star Joseph. He has a level 8 Ekans. You get 384 Pokédollars for winning.
Afterward, Joseph gives you TM01 Work Up. Unlike in past Pokémon games, TMs don't get used up. You can use them as many times as you want.
Go to the Office
There will be an announcement telling you to go to the office on 2F of the school. Go into the school and go up the stairs.
A teacher will be standing near the stairs. Go to the left. A student in the second classroom will give you a Potion.
Now go toward the stairs and approach the teacher. She congratulates you on defeating her students and asks you to battle her. If you are ready, say yes.
Teacher Emily has a level 10 starter that is strong against your starter (Litten if you chose Rowlet, Popplio if you chose Litten, and Rowlet if you chose Popplio). You get 480 Pokédollars for winning. Afterward, she gives you five Great Balls.
After that, Professor Kukui arrives with Captain Ilima, whose trial is held in Verdant Cavern.
Now Lillie will lead you to see more of the city. But first, Kahuha Hala asks you to pet the Tauros that has been blocking the road. Try to pet its face. Afterward, the Tauros leaves with Hala. Now you and Lillie and Hau will go see the city. Go northwest to reach Hau'oli Beachfront.