Is there a way that I could export an application that I created in an AE Server to a different AE Server?
The best way to transport some applications between one client to another is to use the transport case.
This is a functionality used on the "user interface" GUI.
But if you do not have it installed yet you can still use the "export" functionality directly on the ARA interface.
If you plan to move all the objects from a server to another one, it should be easier with the "transport case".
You will find below some documentation about this "transport case" functionality: