We might think that a clean break with all old covenant practices was in order so as to emphasize the fact that it is through the blood of Christ that we can draw near to God (see Hebrews 10:19–25). Nevertheless, it is clear that the apostles (and other believers, see Acts 2:46) continued to go to the temple. It is not clear if they participated in the prayers being led by Jewish priests or simply used those times for their own gatherings.1 Either way, their presence at the temple served to highlight the continuity of the new and the old covenant. The good news of Jesus was not a new religion. The apostles were not calling on Jews to turn their backs on the Lord or to forsake the Old Testament Scriptures. Instead they were proclaiming that Christ is the fulfillment of Scripture and that the Old Testament, when rightly understood, is all about him. By continuing to meet at the temple for prayer the early church is visibly demonstrating their connection with past revelation. They are still worshipping the Lord who has revealed himself to Israel; they have not forsaken him.
1 Now Peter and John were going up to the temple at the hour of prayer, the ninth hour.