Turkish Airlines have quite a lot of destinations throughout the African continent which would of course require overflying Cyprus.
http://www.turkishairlines.com/#
Contrary with the requirements of the EU customs agreement, Turkey does not permit Cypriot Registered aircraft to enter Ankara FIR.
As a result, it would seem reasonable that all Turkish Aircraft are not permitted into the Nicosia FIR.
But if they are allowed, it would also mean that Turkish Airlines are required to contact Nicosia Centre for Airways Clearance.
Do Turkish Airlines get clearance from Nicosia as is required by ICAO? If they do not, then they are non-compliant with ICAO. In other words, Turkish Airlines are illegally using RoC airspace currently under RoC control. If they do, then they recognize the RoC.
If they are not permitted into RoC airspace, and have to circumvent Nicosia FIR and go round it, then the economic cost to Turkish Airlines would be enormous.
What is the RoC's policy on this?