After taking the Magicites of the last Espers out of the Magitek Factory, you can use the Airship to explore the world, then go to the Cave to the Sealed Gate.
Terra's Morph/Trance Ability
After the Magitek Factory, Terra gained an understanding of her half-Esper nature, and as a result, she can now use the Morph/Trance ability in battle. Morph/Trance will be disabled until Terra has earned at least 8 Magic Points/Magic AP. Then if you use Morph/Trance, Terra will temporarily transform into her Esper form. A green countdown bar will show you how long Terra will stay in her Esper form. While transformed, Terra's attacks are twice as powerful, and her magic defense is twice as strong. The more Magic Points/Magic AP she earns before transforming, the longer she will remain in Esper form in battle.
After Terra users her Morph/Trance ability, press Y until her action menu appears again. This allows you to give her a command soon after she transforms.
Learn More Rages
If you wish, you can take Gau to the Veldt to learn more Rages, now that you have encountered more enemies.
Buy an Esper, or Not
In Tzen (in the northern part of the Empire's continent), you can go to the northeast trees to find a bandit who is selling an Esper. It's expensive, and you can get it cheaper later, so it is your choice.
Early in the game, some Moogles helped Locke rescue Terra. One of those Moogles was Mog. Now that you have the Airship, you can get Mog to join your party.
First, go to Narshe. It's on the northern continent, north of the big desert.
When you enter Narshe, go north and there will be a cutscene where Banon and Arvis will tell you that you have to go to the Sealed Gate to get help from the Espers against the Empire, and Terra is the only one who can negotiate an alliance.
After that, go to the house in the southeast of Narshe, and Lone Wolf will be there. Talk to him, then when he disappears, go north up the middle of Narshe (along the same path where Terra went with Vicks/Biggs and Wedge at the beginning of the game) and go into the mines. (You might notice something moving near the entrance to the mines, other than Lone Wolf. It wasn't your imagination. There will be more about that later in the walkthrough.) Inside the mines, go north, then east. From here, just follow the path until you are on the cliffs where you defended the Esper from the Empire. Keep going north and you will find Mog and Lone Wolf.
Walk up to Mog and Lone Wolf, and then after Lone Wolf tells you not to move, wait a while until the two fall to either side of the cliff. Talk to Mog to have him join your party. (If you talked to Lone Wolf instead, you would get a Gold Hairpin, and would not be able to get Mog to join you. You can get Gold Hairpins later in the game.)
Learning Mog's Dances
Mog's special move is Dance. He can learn dances based on the terrain where you fight enemies. You can have him learn all but one of his Dances now.
- Wind Song/Wind Rhapsody: With Mog in your party, fight a battle in the Veldt or any grassy area of the overworld.
- Forest Suite/Forest Nocturne: With Mog in your party, fight a battle in the Phantom Forest or any forested area of the overworld.
- Desert Aria/Desert Lullaby: With Mog in your party, fight a battle in the desert of Figaro, which is south of Narshe. Or fight a battle in any desert area in the overworld.
- Love Sonata/Love Serenade: With Mog in your party, fight a battle in Zozo.
- Earth Blues: With Mog in your party, fight a battle in Mt. Kolts/Mt. Koltz, which is east of South Figaro.
- Water Rondo/Water Harmony: With Mog in your party, fight a battle in the Lete River/Lethe River (accessible from Banon's room in the Returners' Hideout, which is southeast of Narshe. Alternatively, you can fight the battle in Serpent Trench.
- Dusk Requiem/Twilight Requiem: With Mog in your party, fight a battle in the Narshe Mines, South Figaro Cave, or the cave areas of Mt. Kolts/Mt. Koltz.
- The eighth dance can't be learned until later.
Visit New Areas
With the Airship, there are other areas that you can explore to fight new monsters. One of these is the forest west of the Veldt, where you can fight Grenades.
You can also go to the area east of the Veldt to fight Baskervor/Briareus, Cephaler/Devourer, and Chimera.
You can also go to the triangular island in the northeast of the world map, where you can fight Intangir. It is difficult to defeat, however. Try casting Stop on it, then using physical attacks against it.
After you are done exploring, you should go to the eastern part of the Empire's contintent. In the west side of the eastern mountains, you can enter the Cave to the Sealed Gate.