I came back to WoW last year with a new account. This weekend I finally decided to dip into Pet Battles. My character is level 70 and was not boosted or faction changed.
To my surprise, the NPC that starts the pet battles related quests (Varzok in OG for Horde) didn’t have any quests. No pet battles related quests in my log, either.
After googling I found a workaround (from 3-4 years ago, so this issue is not new): I had to make a new, second character, go to Chromie and change the timeline (I picked Cataclysm), and now that second character started to receive quests from Varzok. These quests show in my regular’s quest log as well and I can do them there.
However, after every of Varzok’s quests, I have to switch to the second character to pick up the follow quest as my level 70 character does not get them offered. I cannot change the timeline on my level 70 character, either.
After doing the first three pet battle quests this way (logging in back and forth), my main character suddenly discovered the “Varzok” quest. After this point, Varzok would offer my all further quests (like “Zunta, The Pet Tamer”).
edit: After defeating the tutorial battle trainers and turning in the quest at Varzok, he once again didn’t offer me a follow up quest. I logged back onto my newly created character, and the next quests (like Battle Pet Tamers: Kalimdor) were available. I suppose I’ll just park my level 10 character there!