• Complete playlist activities with your Stasis subclass equipped.
• Use Stasis abilities in playlist activities. Defeating Guardians grants the most efficient progress.
"This is a bit unusual, I know—but the Skeleton Key is not yet fully empowered, and we have an opportunity here to test our Stasis skills on ourselves. If you feel comfortable with that, of course. If not, continue to empower it through our enemies. It never hurts to thin their ranks." —The Exo Stranger
The Exo Stranger wants you to further empower the Skeleton Key so you can decrypt more of Clovis's journal. Do so by using Stasis to defeat combatants or other Guardians. Playlist activities such as Crucible or strikes should give you that opportunity.