You don't say how old your child is, but I'll share my own experience with a similar relocation when I was nine years old. I moved from a school in Texas, where the students' parents largely worked at NASA, to a rural school in Virginia where resources were slim. In fact, because of my birthday and my advanced schoolwork, I skipped a grade after my first year in Virginia. I would not recommend that as a solution for all children, but it did help in my situation.
The main suggestion I would make is to encourage children in this situation to get involved in anything extra in which they are interested, and hopefully find a mentor at the school who will help push them. I was lucky in that way to find such a person in my fourth grade teacher when I arrived. She teamed me up with the choir teacher immediately when she discovered my love of music. I missed part of some classes to assist with a special education music class once a week. And when the choir teacher was absent at the Christmas program, I had enough self-confidence--based on their prior encouragement--to request that the principal let me direct the choir for the performance.
My point here is that if children show initiative in areas they are interested, good teachers will recognize that and push them to excel and expand their horizons. Individualized programs can be created and tailored to a student's needs, even if there are not structured gifted and talented programs in place. If this does not seem to be happening on its own after awhile, you may want to talk to the teacher and ask if your child could explore certain areas of interest at school on a deeper level. Most teachers will respond favorably to such a request.
One positive way to present this idea is to suggest ways that your child could learn more on a certain topic and then present that knowledge to the class in some form. Therefore, you are not creating more work for the teacher, but instead helping the teacher educate the class while showing the teacher the depth of your child's quest for knowledge. Good luck!