You have distributed tools to the people gathered at the Top Rung so they can help toward building the Talos.
This quest is available if you have completed the quest Rich Veins of Hope.
Starting the Quest
Talk to Alphinaud in Kholusia to begin the quest.
To be continued...
Speak with Y'shtola
Go north through the archway, then go east to where the orange arrow is pointing in the minimap. Talk to Y'shtola to proceed. There will be a cutscene.
Speak with Y'shtola Again
Talk to Y'shtola to proceed.
Imbue the Heartstone with Magick
Check on the sparkling Familiar Heartstone to proceed. There will be a cutscene.
Speak with Chai-Nuzz
Talk to Chai-Nuzz to complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Chai-Nuzz to accept the next quest: A Breath of Respite.