It will come up anyway in your security clearance as you have to give all parent/step parents details too which are all investigated, be honest right from the start rather than get so far and your application be scrapped
Aaa, you'd be surprised how deep a security clearance goes.
Honesty is the best path to tread. Lie and the sh1t will hit the proverbial fan and the only loser will be yourself.
Failure to declare can and most likely will lead to all sorts of problems in the future.
I would simply leave it out, I don't intend on ever visiting that country again so no harm could come of it right? I don't see why I can't make a pledge or something to never visit that country instead of having to get a lot of paperwork and do a lot of travelling. I am very honest by nature, so this would be the only lie I'd tell if it came to it.
Your previous application is digitally retained for ten years under data protection legislation and a follow-up application will migrate and carry over your dual Turkish nationality to a second application for Navy, Army or Air Force submitted anywhere in UK.
Mate, pull your head in, get a measure of loyalty, and get a measure of life. Her Britannic Majesty's Forces do not need clowns who cannot or will not swear total loyalty to the Crown. And just as a matter of interest: Why would you want to serve in the Royal Navy, but hide a secret loyalty to another foreign power? Something highly suspicious about your motives in my eyes.