There are many different costumes to choose from in Tales of Vesperia: Definitive Edition, and there are even many that never appeared outside of Japan until this newly Definitive Edition was released. Anyway, before you can change the costumes on your characters, you will need to obtain them. There are so many different things that award costumes in the game, so we won't go into detail about each of them, but it's just something to have in mind. So if you don't have a cool costume for your character yet, don't worry, you might soon get one.
In order to change your costumes, you will need to change your title, since titles are directly connected to costumes. Go to the main menu (Triangle for PS4, Y for Xbox, or X for Nintendo Switch) and select the Status menu. Click on the Title option, and look for titles that have a small clothing icon next to it. This icon indicates that there is a costume tied to this title, so try it on and see if you like it.
And that's all there is to it! Just return to the Title menu later if you want to change costumes again, since you can do it at any point during the game.