We first meet Saul at the stoning of Stephen.
Acts 7:57 Then they (the Jews) cried out with a loud voice, stopped their ears, and ran at him with one accord; 58 and they cast him out of the city and stoned him. And the witnesses laid down their clothes at the feet of a young man named Saul. 59 And they stoned Stephen as he was calling on God and saying, "Lord Jesus, receive my spirit." 60 Then he knelt down and cried out with a loud voice, "Lord, do not charge them with this sin." And when he had said this, he fell asleep.
Acts 8:1 Now Saul was consenting to his death. At that time a great persecution arose against the church which was at Jerusalem; and they were all scattered throughout the regions of Judea and Samaria, except the apostles. 2 And devout men carried Stephen to his burial, and made great lamentation over him. 3 As for Saul, he made havoc of the church, entering every house, and dragging off men and women, committing them to prison.
Stoning was an energetic affair and Israel is a hot country. Those doing the stoning removed their outer garment to facilitate the action. To avoid someone stealing their outer garments they left them with Saul, a pharisee and one they could trust, to look after them.
Saul, being a pharisee, agreed wholeheartedly with the stoning of Stephen
When Jesus appears to Saul on the road to Damascus, Saul says:
Acts 22:20 And when the blood of thy martyr Stephen was shed, I also was standing by, and consenting unto his death, and kept (in the sense of guarding) the raiment of them that slew him.
I hope you find this helpful.