A stable master in Hearthstone. "Takes way better care of her pets than her brother, Unstablemaster."
Stable masters are NPCs that offer a number of pet-related services.
Stable masters are typically found outside most city and town inns or near the pet trainers. You can ask the city guards where they are when you are in major cities. In other locations where city guards are not present the minimap tracking feature will show a horseshoe icon () at their locations.
Stable masters offer hunters the opportunity to store up to 50 pets and retrieve them at any other allied stable master. To stable a pet, right-click on the stable master to open the stable window. You will see your current pet displayed as an icon on the left side of the window. Below that are four slots. Depending on if you purchase to open the slots, they will be either active, or red to show you still need to unlock them. The cost of the stable slots is as follows: 5 for the first, 5 for the second, 50 for the third, and 150 for the fourth. Just click and drag your current pet's icon to any stable slot on the right to stable it. If another pet is in that stable slot, that will now become your active pet.
Players can use stable masters to recover lost non-combat pets rewarded by quests at any stable master. Restoring a lost pet will not reward the pet item, but rather store the pets' spell directly in the pet collection. E.g. [Worg Carrier] – Quest Reward from [59D] Kibler's Exotic Pets can be restored if you destroyed the item but have finished the quest.
* Zybarus of Darnassus is only available after completion of the quest [72] Flight of the Wintergarde Defender.
** Bonnie Hennigan is only available after completion of the quest [84] Aiming High.
*** Nalesette Wildbringer is currently broken and has no stable service.
* Kari the Beastmaster turns friendly after completion of the quest [79] The Crone's Bargain
** Imhadria is only available after completion of the quest / [80] If He Cannot Be Turned
Speculation
This article or section includes speculation, observations or opinions possibly supported by lore or by Blizzard officials. It should not be taken as representing official lore.
Ostler[1] is probably another term for stable masters.
Patch changes
Patch 5.3.0 (2013-05-21): Hunters now have 50 pet stable slots, up from 20.
Patch 5.1.0 (2012-11-27): Stable masters no longer have a cooldown when healing battle pets.
Patch 5.0.4 (2012-08-28): Stable masters now offer to revive companions for 10, as part of the Pet Battle System.
Patch 3.0.2 (2008-10-14): Lost pets and mounts (one time quest rewards) can now be recovered by visiting a stable master. Stable masters can now also accommodate two additional pets.
) at their locations.
I'd like to stable my pet here.
for the second, 50
[Worg Carrier] – Quest Reward from 
[59D] Kibler's Exotic Pets can be restored if you destroyed the item but have finished the quest.
Alliance stable masters
[72] Flight of the Wintergarde Defender.
Horde stable masters
[84] Traitor's Bait.
Neutral stable masters
Patch 5.3.0 (2013-05-21): Hunters now have 50 pet stable slots, up from 20. 
Patch 3.0.2 (2008-10-14): Lost pets and mounts (one time quest rewards) can now be recovered by visiting a stable master. Stable masters can now also accommodate two additional pets. 
