When a case is pending like this. Litigants can ask for a stay from the judge pursuing the case (Hannen) and/or ask a superior court for a stay (5th Circuit).

I'm not sure if the administration pursued an emergency stay (unlikely since I haven't come across it anywhere) with either Hannen or New Orleans 5th. That means it'll probably be weeks before the 5th Circuit will consider the request for a stay and doubtful that Hannen will stay his own injunction.

As was mentioned before, it can be a real f up if Hannen is looking at running out the clock by not deciding on this case and letting his injunction stand. The only way forward is for the 5th Circuit to remove the injunction in the coming weeks. If they don't then it'll stand until a decision (if it ever is) made.