Wrong part of the hemisphere. Right now, the only "NATO" nations providing support are the UK and US along with France. France is not NATO and has its own interests here. Perhaps maybe to prove the Rafale doesn't suck.
Let's be honest. In all-out fight, the Iranian Navy does not stand a chance against the US Navy.
President Trump has been clear: leave our bases alone, we'll leave you alone. Yeah, I get it, ok? The US is providing other support but for the time being, there are no American boots on the ground or "Thirty Seconds over Tehran" moments.
But as the the remainder of NATO? Not going to happen. They are too busy trying to deal with the fact they may have to deal with Russia at some point. And a lot of them are no real friend of Israel.