The new government system that would be created to handle the foreign affairs of the four independent states on the shared island could be called a "federal union" or a "confederation." A federal union is a political system in which multiple independent states come together to form a new, central government, while retaining their sovereignty and autonomy over internal affairs. A confederation is a similar system, but with even greater emphasis on the autonomy of the individual states, and with the central government having limited powers, often only related to foreign affairs and defense. In this case, it sounds like a confederation might be the more appropriate term to describe the new government system.