Against whom did Saul begin his persecution after Stephen's death?
After Stephen's martyrdom, Saul of Tarsus began persecuting the believing Jews in Jerusalem, the Ecclesia called out of Judaism yet still under its umbrella. Not satisfied with Jerusalem and Judea, he then sought to go after the believing Jews at Damascus, believing he served God by stamping out faith in Jesus of Nazareth.
Les explains that after Stephen was martyred back in chapter 7, Saul of Tarsus began his rampage against the believing Jews at Jerusalem. These were an Ecclesia, a called-out assembly, called out of Judaism but still under the umbrella of Judaism; they had not separated from the Law or temple worship. Not satisfied with what he had accomplished in Jerusalem and Judea, Saul wanted to go after the believing Jews up at Damascus. He did all this in the name of religion, thinking he was doing his God a service by stamping out any believing in Jesus of Nazareth.