Subjected to His Will
This quest will be available after Here Lies The Abyss whether or not Cole was in your party when you traveled to Adamant Fortress. You activate this quest by looking for Cole at the top of the Skyhold tavern. Cole is concerned that it may be possible for the Venatori to bind him because of his nature as a spirit so he wants Solas to bind him, and he refuses. Instead Solas recommends finding an amulet that can protect Cole from being bound by Venatori and used against the inquisition like the Greywardens were.
After finding the amulet with a War Table operation you will meet with Cole, Solasn and Varric about what is going on. Varric and Solas play a large role in this side quest and also have very different ideas about Cole and the best way to remedy his situation. You're journey leads you back to Redcliffe where the truth about Cole is revealed and an important decision about his future needs to be made. Turn Cole into a human or help control his spirit? Choose wisely.
GAMER TIP: Even though this is a Cole mission, siding with Solas the entire time will greatly improve your approval rating with him. This includes considering Cole a friendly demon during conversations at Skyhold, and preserving his spirit during the conflict in Redcliffe.
Alternate Post-Quest Outcomes/Events
Preserving Coles Spirit
Going out with Cole as a Spirit
Cole Becomes Human
Going Out with Cole as a Human