Would technically have to be a new one, NATO wasn’t designed to handle this sort of scenario. Of course New NATO would be an America-free roughly equivalent, with some different governance to prevent things like a single county impeding something everyone else wants.
It would be the end of NATO as it stands, there’s no reason the remaining countries couldn’t continue the alliance or start a new one.
Would technically have to be a new one, NATO wasn’t designed to handle this sort of scenario. Of course New NATO would be an America-free roughly equivalent, with some different governance to prevent things like a single county impeding something everyone else wants.