Any Tier 3 gate that I didn't complete before the Mission Update is locked in the Arcade tab of the mission interface. They're also locked if I try to use the elevator in the Arcade.
The only gate for which I have access to Tier 3 is the gate I used to visit the Core earlier this week.
Before the Mission Update, I had Tier 3 clearance.
In case anybody has the same problem: I resolved the issue by going through Tier 2 at one of the gates and talking to the knight at Emberlight.