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