Pharisees specifically weren’t the priests. They were one of the branches of judaism who didn’t think temple was necessary for proper worship (which is why they became the predominant branch after the destruction of the temple and rabbinic judaism stems from them), while temple was where priests worked and performed their rites. If you open your Bible to any of the four gospels, you will find that they say it was the priests who brought Jesus to Pilate.

Also, you shouldn’t take gospels at their word for what they say about Pilate as they insert their theological concerns into Pilate’s judgement. If you read Josephus, he clearly states Pilate condemns Jesus for claiming to be a king, ie. for political uprising, and even Mark, the earliest of gospels, doesn’t state that Pilate didn’t think Jesus guilty, unlike the other three.