Updated to Game Version 2.34.0, Asset Version 451 (January 31st, 2024).
Trainers are NPCs that have their own Mortys that you can battle against. Take the portal at the Citadel of Ricks in Campaign mode and you will find them scattered around dimensions. Every dimension has one Rick and multiple non-Rick trainers. You can also battle Council Members in the Council chamber in the Citadel of Ricks when you have enough badges.