Is there a name for a group of priests?

This only tangentially answers your question, but the group of priests belonging to a given diocese is called the presbyterate from the Greek word for “elder”, whence the English word “priest” comes. read more

In the Church of Jesus Christ of Latter-day Saints, a group of priests is a quorum. Quorum: The word quorum can be used in two ways: (1) A specified group of men who hold the same office of the priesthood. read more

An assistant priest is a priest in the Anglican and Episcopal churches who is not the senior member of clergy of the parish to which they are appointed, but is nonetheless in priests' orders; there is no difference in function or theology, merely in 'grade' or 'rank'. read more