This verse is describing Joseph of Arimathaea, a member of the Sanhedrin (the Jewish ruling council) who is later known for providing the tomb for Jesus' burial. Let's break down the components:

(he had not consented to their counsel and deed): This is the key point. It means that Joseph of Arimathaea disagreed with the Sanhedrin's decision to condemn Jesus to death. While he was a member of the council, he didn't support the plan to have Jesus crucified. This highlights his integrity and possibly suggests a secret sympathy or belief in Jesus.

(from Arimathaea, a city of the Jews): This identifies Joseph's hometown as Arimathaea, which was located in Judea. The phrase "a city of the Jews" simply emphasizes that it was a Jewish community, rather than a Roman or Gentile city.

(who was also waiting for God’s Kingdom): This reveals Joseph's religious and political leanings. "Waiting for God's Kingdom" means that he was a devout Jew who hoped for the establishment of God's reign on Earth, a time of justice, peace, and deliverance for the Jewish people. This could mean he was looking for the Messiah. His actions in burying Jesus later suggest he may have believed Jesus was that Messiah.

In summary, this verse paints a picture of Joseph of Arimathaea as:

A man of integrity: He didn't go along with the crowd and opposed the wrongful condemnation of Jesus.
A respected member of the Jewish community: He was from a prominent Jewish city and held a position of authority within the Sanhedrin.
A pious Jew: He was looking forward to the establishment of God's Kingdom, indicating his faith and hope for a better future.

The verse serves to introduce Joseph as a figure of importance and sets the stage for his later role in providing Jesus with a proper burial, showing respect and honor in contrast to the hatred of those who condemned him.