It has been revealed that TUSAŞ has selected a new engine for the
HÜRJET-D, which will take off from the MUGEM.

TUSAŞ requested the 'Super Hornet engine' F414 from General Electric for the naval variant of HÜRJET.

Defense aviation editor Tolga Özbek:
TUSAŞ has said, 'We want the F414 engine for HÜRJET, which has more thrust than the F404.'
General Electric has made the necessary presentations regarding this engine, and the process for the sale of these engines has begun as requested. The first step has been successfully completed.
It would seem things are moving RAPIDLY, this is not going to be a new 2 engine design, it will be single engine and the engine has been selected as the GE-F414.
I don't think the development process will be that long if its an existing design being modified. Only the landing gear and arresting gear and modifications to the airframe would be needed. They will likely start with launches from a slope on land.
It would be quite funny if we see this be ready before the HAL Tejas-Naval variant. lol