Why do you think you need the services of an executive search firm? What do you expect them to do for you that you can’t do? You likely have many contacts that you can call upon to help you to move into the international entertainment market.
The most obvious route would be to request a transfer to an international bureau of your current employer. If this isn't an option, you'll need to do some homework. Define clearly what part of the entertainment business you want to work in, i.e., television, radio, motion pictures, etc. Then narrow the skills you want to use. Decide what country and city you most want to live and work in, and finally, contact at least five people you know and admire and see what suggestions and leads they can provide for you. Once you've taken these four steps, you'll have a clear idea how to move forward.