I looked ten pages into posts and didn't find the same exact issue.

The "Restoring Trinity" quest I am unable to finish. I've restarted from a previous auto-save and then an earlier save as well. Always when I get to the actual initiation where Karliah is supposed to pull a chain where we enter into a room, she turns around and leaves instead. I've done this quest on PS3, but it is not working for PC. PS3 freezing has prevented me from continuing, but now this quest is preventing me from playing on PC.

I've tried using the wait feature and left the area to return later. Nothing seems to work. I don't know if there is a command I can type to bypass a single quest but I really enjoy this storyline and would like to continue it. I've seen this exact issue posted online, though there does not seem to be a fix for it.

I had similar problems with this quest. In my case, Karliah would not follow me into Nightingale Hall and Brynjolf was nowhere to be seen. It required some console acrobatics, but I was able to get them both there, walking, and into their armor. But when we got to that gate, she wouldn't open it.

Ended up having to bite the bullet and use the setstage command to finish that part of the quest.