Gleaning information from both the aforementioned trailer and the game's official website, here's what we know about Persona 5: The Royal so far (thanks Twitter user BlackKite for compiling this):
The red haired girl shown in the previous teaser is named Kasumi Yoshizawa. She's an entirely new character and party member. In battle she appears to use a sword and a lever action rifle. Contrary to some speculation, she is not a female version of the main character.
There's a new confidant called Takuto Maruki, who you can build a social link with. He's the school counsellor at Shujin Academy.
The expanded story of Persona 5: The Royal will include a whole new third semester, which in Japan, takes place from January to March. Supposedly, this means that the story will carry on quite a bit longer after the end of the original game.
There are a number of new locations that you can visit, both alone or as you develop social links.
Characters will now post photos as well as text in the Phantom Thieves' mobile group chat.
There are new social events with existing characters.
You'll be able to find more powerful enemies wandering around palaces (the game's dungeons).
Palaces appear to have been remixed somewhat, with new locations and new treasures to find.
The Royal will feature some new music tracks.
There will be quality of life changes, such as the ability to check your progress with social links, protagonist stats, and more while exploring the game's world.
Persona 5: The Royal will boast PS4 Pro support, although at the time of writing, it's unclear what this will be. We're assuming it'll be a boost in resolution.
We're sure to learn more and more about Persona 5: The Royal over the coming months, since it's due out in Japan later this year. A Western release has also been confirmed, although we're going to have to wait until 2020 to get our hands on the game.