John Calvin Commentary Acts 13:3

"Then, when they had fasted and prayed and laid their hands on them, they sent them away." — Acts 13:3 (ASV)

When they had fasted and prayed. To obey the oracle, they not only sent Paul and Barnabas away but also, with a solemn rite, appointed them to be the apostles to the Gentiles. This was undoubtedly a public fast.

Luke had previously said that they were fasting, since they were engaged in their ministry; this might have been according to custom. But now there was another reason: by appointing a public fast, which was customary in difficult and very important matters, they stirred both themselves and others to earnest fervency in prayer, for fasting is often mentioned in Scripture as an aid to prayer.

Because it was a matter of such importance to establish the kingdom of Christ among the Gentiles, the teachers of Antioch, not without cause, earnestly prayed to the Lord that He would enable His servants. The purpose of their prayer was not that God would, by His Spirit of wisdom and discretion, govern their judgments in choosing—because all dispute or doubt concerning this matter had been removed. Instead, they prayed that God would equip with the Spirit of wisdom and strength those whom He had already chosen for Himself; that He would strengthen them with His power against all the assaults of Satan and the world; that He would bless their labors so they might not be unfruitful; and that He would open a door for the new preaching of the gospel.

The laying on of hands, which Luke mentions thirdly, was a type of consecration, as we have said (Acts 6:6). For the apostles retained the ceremony that was used among the Jews, according to the ancient custom of the law, as well as kneeling and similar rites, which were beneficial for practicing godliness. In summary, this was the purpose for which they laid their hands on Barnabas and Paul: that the Church might offer them to God, and that they, with the Church's consent, might declare that this office was entrusted to them by God. For the calling was properly God’s alone, but the external ordination belonged to the Church, and this was according to the heavenly oracle.