They won’t be able to make a process in NATO to kick Hungary out because it will require Hungary to agree to adding that process.

The EU has a method to suspend Hungary’s voting rights, which would let them proceed to add other rules without Hungary’s intervention. Canada proposed adding suspension and expulsion mechanisms to NATO back when the treaty was being negotiated in 1948 but after a bunch of debate they were declined. Instead, it was expected that any country that needed to be kicked out of NATO would be in material breach of the treaty. At that point everyone else in NATO would agree that Hungary has effectively withdrawn from the treaty.

I mean, at the end of the day, treaties only have power because everyone agrees that they have power. All of the other NATO powers could spontaneously agree to forget about that old piece of paper they signed and sign a new one instead that doesn’t have Hungary’s name on it.