The Crystal Tower is one of the Chronicles of a New Era sidequest series. To progress through the main story, you are required to complete the Crystal Tower series.
You can begin the Crystal Tower series after you have completed the quest The Ultimate Weapon.
Starting the Crystal Tower Series
Talk to the Outlandish Man near the Mor Dhona Aetheryte in Revenant's Toll to begin the first quest: Legacy of Allag.
Completing the Crystal Tower Series
The final quest in the series is The Light of Hope. This quest is required by one of the post-Shadowbringers Main Scenario Quests, In the Name of the Light.