Why do Turkey and UAE limit the age of aircraft flying over their territory?
Sounds like a market protectionist move by the nations. i.e. The airlines of UAE and Turkey are relatively new. At least their current expansion to a scale that is competitive with the major international airlines is relatively recent. Their airports have also undergone fairly recent expansions to capitalize on their geographical location as hubs between N. America / EU to Asia-Pacific nations. 

I suppose they give their own airlines a competitive advantage by restricting older aircraft. The US / European carriers can only allocate the fraction of their fleet that is new to flights to Turkey / UAE which constrains their activities.

The average fleet age of some airlines in 2013:


Delta  16 years
United  13 years
American + US 13 years
Lufthansa 13 years


Now compare with


Turkish  8 years
Emirates 6 years


Basically, international trade treaties have made it difficult for nations to overtly engage in protectionist measures. So bureaucrats figure out indirect means under the guise of technology, quality etc. that are ostensibly  not favoring domestic industry but are effectively a discriminatory measure. 

Take the numbers with a pinch of salt because airline fleets are continuously upgraded so the average age of a fleet can change pretty rapidly. 

Caveat: The average fleet age may not be representative of the equipment flying international sectors. 

PS. I don't think the regulation has much to do with real safety because safety is concerned with many other factors outside of aircraft age. The safety aspects are better regulated by adopting the FAA safety watch-list based on national assessments. 

At best, this sounds safety theater. Not safety.