Jan, the Chicago Convention is primarily a set of principles. First amongst them is the international freedom of movement.
ICAO,the International Civil Aviation Organization, an arm of the United Nations, was formed by 26 countries to manage how this is achieved and maintained: setting minimum standards of aircraft design and construction, the training and qualification of pilots, navigators, engineers, air traffic controllers and the air traffic system. ICAO membership is now 193 states so covering most of the world. Only by having these agreed minimum standards, which are continuously revised and new ones created, can we freely operate internationally. ICAO doesn't involve itself in national operations.
Each member nation manages it's own internal affairs as it sees fit So we have national permit to fly aircraft and unlicensed aerodromes. Because these standards may vary enormously there is no fixed international agreement and each state may limit international flight of these aircraft to short visits or not at all.