Once you’ve completed the initial set of battles, the next series of Battle Pet Tamers become 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 another Battle Pet Tamer.
The five you will need to defeat in Eastern Kingdoms are:
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)
Completing the second tier of Battle Pet Tamers will open up another quest – Grand Master Lydia Accoste.
Defeating the Grand Master on each continent will unlock daily quests (via an achievement) for all of the other Tamers on that same continent (10 shots a day if you do them all). In fact, you can battle Lydia again as she becomes a daily.
Completing this chain allows access to the Outland series of battles.