To understand the role of the Sanhedrin, we must first know that in Judaism, religion and law were both under the one jurisdiction. Every town in Judea had its own Sanhedrin, or what we would call a district court. Although unclear, these may have been what were referred to as the synagogues in the New Testament. In Jerusalem was the Great Sanhedrin, located within the temple. We would call it the high court or supreme court.
Each Sanhedrin was headed by a high priest, with 22 members selected from other priests, elders or the heads of prominent families. In addition it had scribes and lawyers. The Jerusalem Sanhedrin was larger, with 70 members.
Among their rules, a simple council majority was necessary to acquit someone of a crime. However, a guilty verdict required a vote exceeding the majority. There were no defence lawyers for the accused, and it only required two witnesses for a conviction.
The Romans allowed the Jews to self-govern themselves via the Sanhedrin, with the one exception that they could not execute anyone. The Jerusalem Sanhedrin was also responsible for critical issues such as declaring war, resolving temple issues and investigating false prophets. The members consisted of two groups, Pharisees and Sadducees.
The Pharisees saw themselves as religiously superior to everyone else. They were the lawyers and experts on religious law. They believed the Old Testament prophesies of the Messiah.
They insisted on obedience to the Law of Moses. But they also added additional rules and rituals that became so great in number that Jesus argued with them that obeying all of them was impossible and they had become hypocrites, because even they did not.
Being responsible for censoring the teaching of any new prophet, they closely monitored everything Jesus taught.
The Sadducees were the smaller of the two groups and were the temple aristocracy. They agreed with the written Law of Moses, but not the oral traditions the Pharisees had added.
They did not believe in life after death, angels or spirits and were not looking for a Messiah. Often corruptly dealing with Roman officials, they tended to get appointed the important roles, including that of high priest, giving them control of the Sanhedrin.
They saw Jesus as a threat to their power and if people began to follow his teaching, the Romans may forcefully intervene with the running of the Sanhedrin, destroying the political staus quo. They may even take away their land and hence their nation.
The raising of Lazarus from the dead was the final straw for them.
When the tetrachy was formed in 6 AD, Quirinius, the Roman governor of Syria, appointed Annas as high priest of the Jerusalem Great Sanhedrin. While the Jews did not like that being forced on them, they had no choice but to accept it. And once appointed, a person remained high priest for life.
However, in 15 AD, the Romans replaced Annas with his son-in-law, Caiaphas. This enraged the Jews and they never accepted his authority, staying loyal to Annas.
Consequently, in the first trial of Jesus, he is brought before Annas. It is only after answering to him that he was brought before Caiaphas, who had said in John#11:49-50, “You know nothing, nor do you consider that it is better for you that one man should die instead of the people, so that the whole nation may not perish”.
So, the corruption of the Sadducees, combined with the political influence of Caiaphas, effectively signed the death warrant for Jesus. The same attitude of the Sanhedrin would continue as Christianity started to develop.