A regulated voltage source rated at 7A is definitely capable of supplying any current lower than that provided the voltage remains the same. so the existing circuit itself would be sufficient for a 1A load. But if you are in need of a regulator with maximum load current limit adjustment, then it needs a different architecture. please clarify your question.
and by the way, if your requirement is to miniaturize an existing 7A power supply then you can try changing the 7A transformer at the first stage to a smaller 1A transformer.