F/A-18 will be out of production soon.Building a whole-ass carrier just for Hürjet? Don't know. This seems like buying a Porsche 911 Turbo S and swapping the engine to a renault one with 100hp.
As much as I think Hürjet will be more capable than people think and a nice lightfighter I do not think it is a aircraft you plan a carrier for your navy around.
Kaan is too big. Leaving the only option to either A. procure from another country (F-35B/C, F-18, Rafale-M, J-31) or TAI will develop a new aircraft.
There are so many question marks right now on this project, especially seeing how it won't get serious until we hit the 2030s. We can speculate but who knows what the world looks like in 10 years.
A few years ago I read that KAI foresaw a navalised KF-21 being developed.
India's Tejas N proved to have inadequate capabilities for the IN and was abandoned, to be replaced by a proposed Twin Engined Deck Based Fighter design. The TEDBF may be available some time in the next decade.
Could Turkiye develop its own carrier aircraft in time for any proposed carrier?