Zadar has trains to Zagreb but the route has fallen into disuse. There are at least a dozen stops along the way making it a very, very long trip. The best way of getting from Zagreb to Zadar during the day is to take a bus.
Occasionally it is convenient to take a night train and there you're in luck as there is a nightly train with sleeping accommodations. Taking a night train makes sense for saving on accommodation and also if you need to transport a bike.
Otherwise, take a bus or fly.
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