Pula's small Istrian airport handles almost no transatlantic traffic directly, which means every itinerary from Ohio funnels through a European hub, and after years of routing clients and myself through this corner of the Adriatic, I can say definitively: there is no nonstop business class from Cleveland to Pula, and the smartest Cleveland to Pula business class routings run through Frankfurt or Munich on Lufthansa, through Istanbul on Turkish Airlines, or via Zagreb on Croatia Airlines (OU) for the final short hop. Total journey time hovers around 10 hours of actual flying plus connection time, and the choice of hub matters enormously for comfort on this itinerary.
Lufthansa is the workhorse here, and depending on aircraft rotation you'll find either the airline's long-haul business class seat or, increasingly, the newer Allegris cabin on select 787 and A350 routes out of Frankfurt and Munich — worth checking your specific tail number, since Allegris availability still varies by aircraft. Turkish Airlines routes through Istanbul, where their business class lounge is genuinely one of the better ground experiences in Europe, complete with a live cooking station that makes the layover feel like a destination in itself rather than dead time. My insider tip: book the Zagreb-Pula final leg as a separate Croatia Airlines domestic segment when award space on the international leg is tight — the two-segment approach often unlocks business class seats that don't show as available on a single through-ticket search, since OU's regional flights are typically single-class but the perceived value comes from a smoother, uncrowded connection through Zagreb's compact terminal.
Istria is best flown into during the shoulder seasons of April, May, September, and October, both for weather and for softer business class pricing, since summer charter traffic into the Croatian coast crowds connecting flights and pushes premium fares up on the Frankfurt and Munich legs. Given how much these fares swing with hub routing and seasonal demand, setting fare alerts for this specific Cleveland-to-Pula corridor is the only reliable way to catch the shoulder-season sweet spot before it disappears.