From Trogir to Zadar there are plenty of daily bus departure year around, the travel time by bus is about 2.5 to 3 hours. Most buses drive along the coast so you will be able to enjoy picturesque views on the ways (Tip: get a seat at the left side of the bus). If you plan to return to Trogir from Zadar later on, you should consider buying a discounted return ticket, the discount only apply if you travel with SAME bus company both ways, you can see timetable from Zadar to Trogir here.
If you are landing a Split airport you first have to a taxi or local bus from the airport to the main bus station in Trogir, to continue your travel to Zadar