More than 100 years ago, there used to be a sea connection from Split to Zadar, but as better roads were built the ferry routes were closed. But there is hope.. In 2018 the company Envira d.o.o announced they would operate a fast ferry route from Split to Zadar via Sibenik, the operation was scheduled to start April / May 2019, unfortunately something seems to have gone wrong, as the ferry route never came into operation.
So If you insist on travelling by sea, the only option is to charter a boat or hire a high speed water taxi, but both options would be very expensive. The more economical alternative is to take the bus or to rent a car in Split and return it in Zadar.