That will depend entirely on the international school. You'll need to look closely at how the curriculum aligns with the curriculum at your current school.
The international school I'm familiar with is very reluctant to allow accelerations, and indeed many people compare the curriculum to their home curriculum and decide to move the child down a year.
FWIW, this international school is exceptional for gifted children, as the small class sizes and general high level of curriculum allow for significantly better in-class differentiation than average. My K'er gets second grade math in class with the top table and his reading books in class are third grade level with one other top student in the year. This is standard; we needed no advocacy to get this setup.
Contact your school. Compare curriculums and see what they say. It's about getting a good fit, and that's advantageous for both you and the school.
