I am sure that you fully understand the problem but I can’t make head or tail of it from your description. You start out talking about a circular array because you are continuously iterating over the elements but then you talk about removing and inserting elements on a regular basis and an array is not the best data structure for that.
It seems to me you should be considering something like a linked list but without a clearer idea of what you are trying to do I can’t be sure.
Why not try and describe what you want to do with the data without mentioning circular arrays or arrays in general.