In the Wild Area, you can find a roaming NPC who will battle you. She has the starters.
You can also do Champion's Cup Rematches by talking to the front desk person at Wyndon Stadium. These allow you to fight NPCs over again like Raihan, Leon, Allister/Bea, Hop, Marnie, etc. There are also new monotype trainers to battle.
There is also a Battle Tower, which is located in what used to be Rose Tower.
Like all Pokémon games, Pokémon Sword & Shield has got a post-game battle facility. After losing to you in the league, Leon has taken the Rose Tower and transformed it into the Battle Tower. Here, things run a bit different than before. Instead of just battling until you have lost and then starting over, instead it runs similar to Ranked Battle online and features a tier system. Starting with Beginning Tier, it moves up to Poké Ball, Great Ball, Ultra Ball and Master Ball all based on wins. However, if you lose, your placement will drop down and you have to start again.
Of course, there's always Ranked and Casual battles if you're fighting online.
Casual battles can be used for practice and will not impact a player's rank. Ranked battles are where the real competitive action is at.
You can also do Max Raids.