Can countries introduce new aviation policies unilaterally?
Aircrafts need to be certified to operate under FAA/European/Russian... regulations in terms of safety, noise, etc.
For instance, in Europe EASA is the authority "for the airworthiness and environmental certification of all aeronautical products[..]".

Sometimes countries actually want to introduce new policies.
One of the most famous was in 1971, when "The US, India, and Malaysia all ruled out Concorde supersonic flights over the noise concern[..]" as reported here on Wikipedia.

Another one about aircraft noise was in 1999, when "The EU's proposed noise ordinances effectively prevented the use of hush-kit outfitted aircraft in Europe[..]".

So every country already has its own regulation.