A lay movement for keeping the law in ordinary life — popular, meticulous, and the group Jesus argues with most because it was the closest to him.
The Pharisees were not priests. They were a largely lay movement built on applying the law to daily life, with an oral tradition of interpretation alongside the written text, and they believed in resurrection, angels and providence. They were the popular party, and they survived the destruction of the temple precisely because their religion did not depend on it — rabbinic Judaism descends from them. The gospels record more disputes with them than with anyone else, which is generally a sign of proximity rather than distance: Paul was one, and said so in the present tense.