These are Gym Leaders that have Pokemon in the anime that they lack in the games.
I will be counting their teams at battle facilities (e.g., Pokemon World Tournament or the Battle Chateau) and in LGPE, but I will not count their teams in the Stadium games because they pretty much mimic their anime teams anyway. I will also count Pokemon that have made an anime appearance in Pokemon Origins.
Some Gym Leaders have evolutions/pre-evolutions of Pokemon they have in the anime -- if they have an evolution/pre-evolution in the anime but not in the games, I will count it, but not if said Pokemon was a pre-evolution that was seen to evolve in the anime.
KANTO:
Brock has a Crobat, Sudowoodo, Comfey, Forretress, Marshtomp, Croagunk, and Chansey in the anime but not in the games. He also had a Vulpix but he returned it to its OT.
Misty has a Goldeen, Corsola, Horsea, Politoed, Azurill, and a Luvdisc nickname Caserin. There are also multiple Shellder and Goldeens at the gym, alongside a Seel. She does not have any of these in the games.
Erika has an Exeggcute, Oddish, and Bellsprout in the anime but not in the games.
Koga has a Scyther in the anime but not in the games, however this Scyther was only seen in a flashback. There are also multiple Voltorb in the gym that are not in the games.
Sabrina has a Haunter in the anime but not in the games.
Blaine has a Rhydon in the anime but not in the games.
Giovanni had a Charmander in the anime that was only seen in a flashback in Pokemon Origins. He does not have one in the games.
JOHTO:
Falkner has a Hoothoot in the anime but not in the games.
There are multiple Caterpie at the gym in the anime, but Bugsy does not have one in the games.
Whitney has a Nidorina in the anime but not in the games.
Chuck has a Machoke in the anime but not in the games.
There are multiple Shellder at the gym in the anime, but Pryce does not have one in the games.
HOENN:
Norman has a Slakoth in the anime but not in the games.
There are multiple Baltoy at the gym in the anime, but neither Tate nor Liza have one in the games.
Juan has a Seaking, Azurill, Seadra, Goldeen, Wailmer, Corsola, Barboach, Chinchou, Pelipper, Masquerain, two Wingull, two Startu, two Masquerain, and three Tentacruel in the anime but not in the games. Most of these are just for show in an exhibit.
SINNOH:
Gardenia has a Bellossom, Vileplume, and Victreebell in the anime but not in the games, however she only mentions that she has them and we don't see them. She was also given James' Cacnea, and she does not have one in the games.
Byron has an Omanyte, Omastar, Kabuto, Kabutops, Cradilly, and Armaldo in the anime but not in the games.
Candice has a Dodrio in the anime but not in the games. She also had a Turtwig when she was younger, and she helped raise a Glameow that belonged to someone named Zoey -- neither of which are in the games.
UNOVA:
Cilan has a Crustle and Stunfisk in the anime but not in the games. He also briefly had a Basculin but it was released.
Elesa has a Tynamo in the anime but not in the games.
Iris has an Axew, Escadrill, Emolga, Dragonite, and Gabite in the anime but not in the games.
Cheren has a Herdier, multiple Sunflora, Ducklett, and Minccino, and two Shinx in the anime but not in the games.
KALOS:
Grant has an Onix in the anime but not in the games.
Korrina has a Mienshao in the anime but not in the games.
Ramos has multiple Sunflora, Vileplume, Oddish, Bellossom, and Exeggutor at his ranch in the anime, but he has none of these Pokemon in the games.
Clemont has a Bunnelby, Chespin, Luxray, and Magnemite in the anime but not in the games. He also has a Dedenne not seen in the games, and this is under the care of Bonnie.
Valerie has a Spritzee in the anime but not in the games.
Olympia has a male Meowstic in the anime but not in the games, where she only has a female Meowstic.
Wulfric has multiple Bergmite in the anime but he does not have one in the games.
GALAR:
Nessa has made only a cameo appearance in the anime, but she is seen to have a Milotic that she does not have in the games.
Bea has a Sawk, Throh, Tyrogue, Scraggy, Machop, and Machoke in the anime but not in the games.
Allister has made only a cameo appearance in the anime, but he is seen to have a Gastly and Haunter that he does not have in the games.
OTHER:
Blue is a game exclusive character who has the same role as Gary in the anime. I will not be looking at Blue/Gary for this list.
Janine has not been seen in the anime and likely never will.
Lt. Surge, Morty, Jasmine, Clair, Roxanne, Brawly, Wattson, Flannery, Winona, Wallace, Roark, Maylene, Crasher Wake, Fantina, Volkner, Chili, Cress, Burgh, Clay, Skyla, Brycen, Drayden, Roxie, Marlon, and Viola all have Pokemon in the anime that they also have in the games.
Note that most of the Galar Gym Leaders have only made very brief visual or cameo appearances, so their full teams in the anime are not yet known, and as such information on them is incomplete. For a good number of them, so far the Pokemon that we have seen of theirs in the anime is also what they have in the games.
Please let me know if I have made a mistake or are missing any. I have not watched the anime since XY so I will need to be informed when more is revealed for the Galar Gym Leaders and their Pokemon in the anime.