While you do run into your rival, Hugh, periodically over the course of the game, you'll have an opportunity to fight him after beating the game as well. In fact, you'll have two chances.
In Undella Town, you'll find Hugh standing just to the west of the Pokemon Center. Talk to him and he'll give you HM06 (Dive). Additionally, he'll challenge you to a battle!
Like always, his team varies depending on who you started with, although he now has a full team of six Pokemon to take you on with.
After you've beaten Hugh in Undella Town, he'll reappear in Driftveil City, in the ex-Team Plasma Base on the northern end of town. You can battle him once per day, too.
He uses the same team he used before against you, although they've gained a few levels. He shouldn't be overly tough compared to a lot of the other "legendary Trainers," so consider him good practice. Since you can fight him daily, you can use that opportunity to gain EXP and bragging rights against him.