After completing your mission against Team Galactic at Stark Mountain, you can challenge the Battleground where the Sinnoh Gym leaders and your former tag battle partners can be fought against. They are randomly selected each day and can only be fought once a day. Every one of them only uses 5 Pokémon and all of them except Candice and Mira have at least one non-regional Pokémon.
For the Gym Leaders they have higher level teams than what they had before. Pretty much just about the same strategies will work here but just remember some of these Pokémon have moves that can counter their weaknesses.
You can also face against the characters that you teamed up with at different locations throughout the game earlier. Since they do not follow a type specialty like the Gym Leaders, your team must be more diverse before you face any of them. Like the Gym Leaders some of their Pokémon also have moves that can counter their weaknesses. Notably they still have the Pokémon they used before that fought alongside you (though in Cheryl and Miras case, theirs have evolved).