This section, starting at verse 1, fails to name the adversaries of Jesus up until this verse. In the Greek, it appears that it was the ‘Herodians’ who had set up the trap in the synagogue. The Pharisees then advised the Herodians that they needed to destroy Jesus.
At the time of the story, the Ethnarch, or “King of the Jews”, was the grandson of Herod the Great, who had displaced the Hasmonians through the grace of Caesar and legions of Rome. Prior to Hasmonian rule, the area had been a precinct of Syrian Greeks, Egyptian Greeks, and ruled by Persia prior to that. Consequently, there were in that region several competing families, each with different sponsoring powers.
In his book “Wars of the Jews”, Flavian Josephus outlines three social groups operating in Jerusalem at the time: Pharisees, Sadducees, and the Sicarii. Briefly, the Sadducees represented the royal family and preferred to Hellenize their culture, while the Pharisees worked to retain the idiosyncratic Judean cultural dynamics and avoid Greek traditions. Both worked with Rome to varying degrees, and so the Sicarii represented the separatists who refused to work with Rome and opposed both Pharisees and Sadducees.
This verse is thus saying that it was at this point that the Sadducees joined with the Pharisees in opposing Jesus and working for his ruin.