Rabbis aren’t priests – Acharei Mot
Chief Rabbi Solomon Hirschell
Apart from this, only a Jew who is a kohen is a priest, and as far as I know Hirschell was not a kohen though his successors the Adlers were.
But as a general rule, the roles of priests and rabbis are distinct. The priest officiates in the sanctuary: the rabbi is a scholar, teacher and judge. The traditional responsibility of the rabbi does not require him to conduct services though often the modern rabbi does play a liturgical role in the synagogue.
The more important thing a rabbi can do for his community is to be the embodiment of a religious personality whose standards are an example to others.
