What covenant was Israel still under in the book of Acts?
Israel was still under the covenant economy going back to Exodus 19, which is the law. Peter and John going to the temple at the hour of prayer showed they remained under that covenant and had no concept yet of the grace of God that would be poured out later.
Les explains that in the book of Acts, Israel is still under the law and the covenant economy reaching all the way back to Exodus 19, where Israel could be a kingdom of priests if they accepted their king. The temple was not removed from Israel's religious scene until 69 or 70 A.D. From the crucifixion, which he dates to 29 A.D., to the temple's destruction and Israel's dispersion is about forty years, and Acts covers that whole period. Early in Acts, probably just a few weeks after Pentecost, Peter and John go to the temple at the required hour of prayer. This shows they have no concept yet of the grace of God to be poured out later. The lame man is healed, holds Peter and John, and all the people run together to Solomon's porch, which was part of the temple.