Upon arriving at the isle, you’ll notice the lack of a staple of modern WoW: World Quests. This is just a temporary situation.
World Quests in the Coiled Isle are unlocked by progressing in the Patch 12.1 campaign. Namely, you need to finish Chapter 4 of the campaign, Original Sin, and complete the follow-up quest that takes you into the new dungeon, Altar of Fangs.
The path is short: follow your Campaign quests until you reach The Vaults of Atal’Utek: Altar of Fangs, the quest after Chapter 4. You will need to talk to Lady Liadrin at the entrance of the dungeon and then complete the dungeon.
No Group Required
Note that you can complete the quest in a Follower Dungeon; it doesn’t need to be Heroic or Mythic.
Final Step to Unlock World Quests
After completing the dungeon quest, you’ll head back to Tokka’s Landing and take part in a short RP scene to complete Nature of Her Wounds. Completing this quest grants you the 
Coiled Isle World Quests aura, unlocking them permanently.
Unlocking World Quests for Other Characters
Similarly to unlocking The Coiled Isle itself, you only need to worry about this process once. The World Quest unlock is account-wide, meaning all your other characters will have access to them immediately once you complete Nature of Her Wounds.
How Long Until You Unlock Coiled Isle World Quests?
After unlocking the island, you should be able to unlock world quests in about an hour or less of gameplay, which entails completing Chapters 3 and 4 of the Campaign, the Altar of Fangs dungeon, and the quick final quest.
