I believe that if you are a certain point in the Institute's quests, you can initiate the objective after "Continue working for Father". I believe that if you're far enough to get the kill request, then you should be far enough to progress Underground Undercover. First, talk to Desdemona and warn her what you've been ordered to do. I don't know if this actually does something, but it's what I did. Then go back to the Institute. If you run around a bit, a generic gen 2 synth will walk by you and tell you that Z1 is in your room at the Institute. Go to your room and talk to him. If you can't find the synth, you could probably just go ahead into your room.