It is not often recognized that Peter formed the vanguard of gospeling the Gentiles. But in his wake came Barnabas and Saul (aka, Paul):

11:19 Now those who had been scattered because of the persecution that took place over Stephen went as far as Phoenicia, Cyprus, and Antioch, speaking the message to no one but Jews. 11:20 But there were some men from Cyprus and Cyrene among them who came to Antioch and began to speak to the Greeks too, proclaiming the good news of the Lord Jesus. 11:21 The hand of the Lord was with them, and a great number who believed turned to the Lord. 

A good sketch of this passage can be found in Bev Gaventa’s The Acts of the Apostles (Abingdon New Testament Commentaries)
.

Missionally: persecution prompts missional expansion. The persecution under Stephen scattered Christians (messianic Jews) and where they went they told other Jews about Jesus. But some of these messianic Jews began to tell Gentiles the good news too.