Northwest of Levincia, you can go through East Province (Area Three) to find the Poison Crew Base of Team Star.
How to Find the Poison Crew Base
If you go northeast from Levincia, you will reach East Province (Area Three). Continue going northeast on the path until it curves to the west. Go west along the path, then when it turns south, go south. Eventually, the path starts going toward the west. You can go north from there, and optionally battle the Lurking Steel Titan if you haven't already. Then go northwest from that area to find a path to the Pokémon Center of the area. From there, you can follow the path to the west, then turn northwest and follow the path to the Poison Crew Base.
Defeat the Guard at Navi Squad's Base
When you approach the base, there will be a cutscene, and you will be challenged to a battle. You will fight Pokémon Trainer Youssef, who has a level 30 Gulpin and a level 31 Shroodle. You get 1612 Pokédollars for winning.
Enter Navi Squad's Base
If you have defeated the other four bosses of Team Star already, be aware that after you defeat the fifth boss of Team Star, the Academy entrance will be blocked by a Pokémon trainer with high level pokémon.
When you're ready, go to the door of the base and ring the bell. However, you can only bring the first three Pokémon in your party.
About the Star Barrage
Team Star's fighting style is called the Star Barrage. You need to press R to send out multiple Pokémon at a time. You can go back to Clive to heal up your Pokémon. You can also use vending machines to help recover your Pokémons' HP, if you find one. You need to defeat 30 of Team Star's Pokémon within 10 minutes to make Team Star's boss come out to battle you. If you need to exit the challenge early, press Y.
During the countdown, move through the base and approach Team Star Grunts to make them send out their Pokémon. Face the enemy Pokémon and press R to send out your Pokémon against them. Your Pokémon will automatically battle them. They will do better if their type is supereffective against the enemy Pokémon's type. You can press ZR to recall your Pokémon back to you if needed.
Defeat Atticus, Boss of Team Star's Poison Crew
After your Pokémon defeat 30 of the enemy's Pokémon, Atticus will challenge you to a regular battle, where you can use the six Pokémon in your party.
Atticus has a level 32 Skuntank, a level 33 Revavroom, a level 32 Muk, and a level 32 Poison-type Revavroom (the Navi Starmobile).
Afterward, there will be a cutscene where you learn more about Team Star.
You get Team Star's Poison Crew Badge, and a TM102 Gunk Shot. (Press A if nothing is happening.) You'll also get some LP, and more TMs will be unlocked in the TM Machine. You will also receive Pokémon materials that you can use to make TMs.
Explore the Base
After this, you can freely explore the Poison Crew Base, where you will find various items, including TM092 Imprison, TM042 Night Shade, TM090 Spikes, and a Poison Tera Shard.
If you want to play the Star Barrage again, you can ring the bell at the front gate of the base.
If you go northeast from the base, you will find a tent with dropouts from Team Star. Talk to the Grunt in front of the tent to get a Sporty Cap (Star). Next to the tent, you find a TM081 Grass Knot, and a Revive.