You need to finish the war campaign which probably isn’t completely possible until level 50. However leveling through the zones will help. Unlike unlocking the Alliance races, it doesn’t require any group content so it is fairly easy to accomplish solo.
Hello OP, this is a reliable guide for what you’re after.
Essentially, you need to finish the main questline of Zuldazar, Nazmir, and Vol’dun. After that, you need to finish the 8.0 and 8.1 war campaign.
As the poster above me said, you’ll need to hit level 50 to do the war campaign. But if you use BfA as your leveling, you’ll level up by completing the main quest and will be well on your way to unlocking Zandalari Trolls.
“Stormwind extraction” is the quest that will unlock Zandalar, thus put you in the right path.
If memory serves you will have to do the entirety of all 3 zones’ main questlines as well as the war campaign in order to unlock them, though you might get credits for the alliance war campaign. I got my Dark Irons with the horde war campaign, anyhow.