“Then the chief priests and the elders of the people were gathered together in the court of the high priest, named Caiaphas; and they plotted together to seize Jesus by stealth and kill Him.”
‭‭Matthew‬ ‭26:3-4‬ ‭NASB1995‬‬
https://bible.com/bible/100/mat.26.3-4.NASB1995

The government was Rome and Ceasar NOT the priests. Pointus Pilate went along to avoid a rebellion.