After defeating the Elite Four and becoming the newest Kanto Region Champion, you can rematch the Pokemon League whenever you would like. After defeating all four Elite Four Members when challenging the Pokemon League once more, you will again face off with your Rival in order to defend your Championship Title. You will continue to earn loads of Experience and Money when you rematch and defeat the Elite Four, as well as your Rival for the Kanto Region Championship.
Believe it or not, your Rival will actually use the same exact Pokemon Team as when you first defeated him to become the Kanto Region Champion (except at much higher levels). This includes his Pidgeot (that will Mega Evolve), Vileplume, Marowak, Rapidash, Slowbro and Jolteon. All of his Pokemon will now be at Level 66, with the exception of his Starter Partner Pokemon that will be at Level 67.
Since your Rival still doesn't use any one specific type of Pokemon, you will need a balanced team of your own in order to defeat him. A Water Type Pokemon will still do wonders against his Marowak and Rapidash, while an Electric Type will have the advantage against his Slowbro and Mega Pidgeot. Like before, a Flying Type or Fire Type is recommend for Vileplume since they do the most damage to it. And finally, a Ground Type Pokemon should have its way against his Jolteon since it continues to be especially weak to Ground Type Attacks and because its Electric Type Moves are useless against Ground Types. Finally, make sure the Pokemon you do use against your Rival in this rematch are at Level 65 or greater, as this will allow you to match up well against him once again.