Wait for Tannis is an objective in the Story Mission, Cold as the Grave in Borderlands 3
Talk to Wainwright
Meet Clay
Follow Clay
Enter estate
Find the barrel delivery pipe
Secure area
Activate delivery pipe
Oh shit
Destroy barrel
Grab Vault Key Fragment
Enter conveyor system
Meet Wainwright
Defeat Aurelia
Check on Hammerlock
Head to Estate Grounds
Reveal ruins
Activate bridge
Enter ruins
Meet Tannis
Give Vault Key fragment to Tannis
Wait for Key's creation
Take Vault Key
Place Vault Key
Defeat Grave and Ward
Defeat Graveward
Wait for Tannis
Observe Tannis
Loot Vault
Talk to Tannis
Return to Sanctuary 3
Talk to Lilith