After Turkey was taken out of the F-35 aircraft program because of CAATSA sanctions imposed by the United States, it has been trying to develop new solutions to deploy fixed-winged air assets on Landing Helicopter Dock (LHD) Anadolu.
www.navalnews.com
Comparing to an CATOBAR-aircraft carrier, Anadolu’s flight deck is shorter because it was designed for STOVL (short take-off and vertical landing) aircraft. For this reason, the TAI Hürjet may need a catapult system and arresting gear system to be able to operate from the LHD. But if during landing the tailhook failed to catch the arresting cable, the flightdeck will be too short to reach sufficient speed.
So actually they need a STOVL-aircraft like the F-35B to operate from an LHD, or they have to completely redesign the LHD into a CATOBAR-carrier. Its sounds very complicated and expensive to solve this problem, besides that the Hürjet is a advanced jet trainer/light fighter in the same class as the KAI T-50, not a multirole fighter like the Rafale or F-35 which are designed from the beginning to be able to be navalized.
This plan is maybe even impossible to realize with an acceptable budget and ordering a foreign aircraft carrier + naval jetfighter will be probably much more cost effective than to struggle with two incompatible designs.
Unless they want to use the LHD the same way like the Royal Thai Navy uses the Chakri Naruebet : just as a helicopter carrier.