From the perspective of my particular faith:

A priest or priestess of the craft is any individual who has been "properly" initiated into the craft by a craft elder.

Most are contributing members of a Gardnerian coven, and perform whatever functions are required within that framework.

The expectations are specific for each degree, but at the very leat, a first degree will be able to cast a circle and have a working knowledge of the theology and laws of the craft.

Each priest or priestess in Gardnerian craft is a devotee of the Gardnerian God and Goddess. They may also have individual relationships with other gods of other pantheons, but would be expected to grow that relationship outside of the formal Gardnerian rituals.

Gards do not consider themselves to be clergy in a formal sense, since we are all basically equals in the circle, and each is expected to be able to perform most of the required ritual elements of the craft. I have always considered us to be more like a monastic order (without the celibacy or seclusion). This is my own take on my faith, others may have a different view.