The Galar region will be using a different format for its Pokémon League than the other regions in the Pokémon series, so Pokémon Sword & Shield will not feature an Elite Four.
The regions in the Pokémon series have generally used the same rules regarding the Pokémon League. The Pokémon Trainers in each region need to travel the land and defeat the eight different Gym Leaders in order to earn a Badge from each of them. Once the player has gathered the eight Gym Badges, then they have earned the right to challenge the Elite Four in a series of sequential battles. If the player can defeat the Elite Four, then they can challenge the Champion of the region. The only games that have deviated from this format are the ones set in the Alola region, which didn't feature the Gym Leaders but did include the Elite Four.
It seems that the Galar region from Pokémon Sword & Shield eschews the use of the Elite Four, as a new update on the official website for the games has outlined the rules for the Galar Pokémon League. According to the update, the Pokémon Trainers who gather eight Gym Badges will earn the chance to enter the Champion Cup, which is a televised tournament that offers the winner the right to challenge the current Champion.
The switch to a tournament format might be another reference to soccer, as many of the biggest soccer events use a similar format. For example, the FIFA World Cup starts out with round-robin teams before it moves on to a knockout tournament.
The absence of the Elite Four will be a first for the series, as they have acted as a barrier to victory since the days of the Kanto Elite Four in Pokémon Red & Blue. The Elite Four have offered some of the most challenging battles in the history of the series, with many Pokémon fans still wincing at the memories of the likes of Drake and his vicious Salamence in Pokémon Ruby & Sapphire. It's likely that the other opponents in the Champion Cup will act as proxies for the Elite Four battle, as only the best trainers in the Galar region are chosen to participate.
Source: Pokémon Sword & Shield