After the ones received in the main story, you can get rare league cards of the Gym Leaders helping them in the post-game tasks. You can get Chairman Rose's rare league card by talking to Oleana in the Galar Mine. You can get Leon's rare league card by beating him in the battle tower. Ball Guy will give you their League Card after becoming champion if you talk to him outside Motostoke Stadium. After defeating Marnie in the rematch in Spikemuth as gym leader, you will receive her Rare League Card. After defeating Hop the second time in Slumbering Weald you will receive his rare league card. You get Piers's League Card after catching the box legendary.
In the DLC, Honey's league card and rare league can be obtained by donating 800,000 and 3,280,000 Watts respectively. Klara or Avery's rare league card can be obtained from them in Potbottom Desert after defeating Mustard at the Battle Court. Peony's league card can be obtained by completing your first Dynamax Adventure, and the rare one can be obtained from him by finishing all the Legendary Clues.
Link trading, battling, and just using the swap cards feature in the Y-Com will allow you to get League Cards of other players.
Source: Bulbapedia and experience
