Does the New Testament church have a set hour for prayer?
The New Testament church has no prescribed hour for prayer. Peter and John went to the temple at the ninth hour because they were still involved in temple worship, not because the church was instructed to pray at a set time. Muslims and Judaism had prescribed prayer hours, but the church does not.
Les explains that Acts 3:1 shows Peter and John going up to the temple at the hour of prayer, the ninth hour, just a few days after Pentecost. No one had told them to stop temple worship; they were still rabidly involved in it even though they had been set apart from mainstream Judaism. The ninth hour was the hour of prayer, and they obediently went. Les raises the question: if this is the beginning of the church, why are Peter and John going to the temple at a prescribed hour of prayer when the church doesn't have any of that? Unlike Muslims, who pray at set times, and Judaism, which did, the church has no instruction that at a certain hour everyone should bow down and pray. So the church does not have a set hour for prayer; Peter and John's action reflects their continued temple involvement, not a church mandate.
Now Peter and John went up together into the temple at the hour of prayer, being the ninth hour.