Once you’ve completed the initial set of battles, the next series of pet tamers in Eastern Kingdoms becomes available from Audrey Burnhep in Stormwind. This is an account-wide but faction-specific quest.

Defeating each one will give you a 5min Pet Recovery debuff, meaning you’ll have to wait out the 5min before you can battle the next pet tamer.

David Kosse
David Kosse <Master Pet Tamer>
Location: The Hinderlands – Stands just off the path between the forked part of the road and Jintha’alor
Level 13 Pets: Subject 142 (Critter), Plop (Magic) and Corpsefeeder (Beast)

Deiza Plaguehorn
Deiza Plaguehorn <Master Pet Tamer>
Location: Eastern Plaguelands – Other side of the lake at Light’s Hope Chapel
Level 14 Pets: Plaguebringer (Undead), Bleakspinner (Beast) and Carrion (Critter)

Kortas Darkhammer
Kortas Darkhammer <Master Pet Tamer>
Location: Searing Gorge – next to the Horde flight master in Thorium Point
Level 15 Pets: Garnestrasz, Veridia and Obsidion (3x Dragonkin)

Everessa
Everessa <Master Pet Tamer>
Location: Swamp of Sorrows – Between Marshtide Watch and Sorrowmurk
Level 16 Pets: Dampwing (Flying), Croaker (Aquatic), Anklor (Critter)

Durin Darkhammer
Durin Darkhammer <Master Pet Tamer>
Location: Burning Steppes – at the base of Blackrock Mountain
Level 17 Pets: Ignious (Critter), Comet (Flying) and Moltar (Elemental)

Once you’ve defeated the above pet tamers, Grand Master Lydia Accoste becomes available.

Lydia Accoste
Lydia Accoste <Grand Master Pet Tamer>
Location: Karazhan – Between the church and the graveyard
Level 19 Elite Pets: Bishibosh (Undead), Nightstalker (Undead), Jack (Elemental)

Defeating the Grand Master Tamer rewards the Taming Eastern Kingdoms achievement which unlocks the daily quests for all tamers on that continent (10 shots a day if you do them all).

Completing this chain allows access to the Outland series of battles.