This video handles the Taming the Beast quest chain from the point just in advance of Thotar provides you with a taming Rod for just a Dire Mottled Boar in Razor Hill. Thotar provides you with a number of 3 taming rods, each differs and allows you tame beasts in the next order: Dire Mottled Boar, Surf Crawler and eventually an Armored Scorpid.

When you have concluded the taming part of The hunt chain, you must head to Orgrimmar and speak to Ormak find more Grimshot inside the Valley of Honor so as to unlock your companion pet handling abilities: have a peek here Tame Beast; Feed Pet; Revive Pet; and Beast Training. WoW Classic Orc Hunter Pet Quest

Last but not least, remember to go to the Pet Trainer and get the Pet abilities that you will have to give to your pet.