This page explains how to start and complete the A Fragmented Monument shrine quest.
How to Start the Quest
Talk to Garini at Palmorae Ruins to start the quest. The Palmorae Ruins are east of Lurelin Village, which you can reach by going east from Lakeside Stable (near Shai Utoh Shrine).
How to Complete the Quest
Check the Kah Yah Shrine page for details on completing the quest.