How do you soundproof a door?
Sound is blocked (or more precise, limited) when two things happens.
First the door must close airtight, which is fairly easy to make with a tightening seal.
Second, the sound must not be able to pass through the door. That is most easily done by replacing the entire door with a heavy, fireproof door (they are heavy and thus soundproof). If that's not possible, a sandwich dampening construction on the door will help a lot, but it should be done right.
You can buy sound dampening mattes that can be glued onto the door, which will help. That would be my best suggestion. Or block off the door entirely.