Why were Peter and the Jewish leaders of Jerusalem losing their influence in Acts?
The Jewish leaders lost influence because Israel kept slipping into unbelief, rejecting Christ as Messiah, His kingship, and His Kingdom. As that system fell through the cracks, God turned to the Gentiles, and Paul's ministry emerged. Consequently, the twelve and Jerusalem elders no longer held the power God had originally entrusted to them.
Les explains that Peter had preached his heart out through the early chapters of Acts, promoting Christ as Israel's Messiah, His coming kingship, and His Kingdom, but Israel rejected it. That was not Peter's fault. Yet in God's divine purposes, as Israel kept slipping, and slipping, and slipping away in unbelief, Peter, the eleven, and these Jewish leaders of Jerusalem naturally lost their clout. The whole system was falling through the cracks. But God was not out of it. As Israel slipped and in unbelief rejected all this, God turned to the Gentiles. So as the Jews were going down, the Gentiles were coming out, and this became Paul's ministry. Those who seemed to be somewhat, the twelve and the elders at Jerusalem, no longer had the power rightfully as God had entrusted it to them.