A priest, in the anthropological sense, is a full-time religious specialist who acts as a representative for a society's deity or deities. Priests are generally associated with societies that have attained at least the complexity associated with regular agriculture.
Priests perform regular or cyclical rituals that ease the supernatural relationship between human and god. Unlike shamans, they don't typically address issues between individuals and deities, but rather speak as a mediator between the entire society and the gods which rule the earth.
Priests have a liturgy—a specific text or set of texts that they follow, which may include creation stories, rules and ritual calendars. They produce statues and carvings of the deities; they have standardized ritual paraphenalia that is found within a broad region. Musicians are often associated with priests.
This definition is a working one used by anthropologists to put a name on something that is eccentric to each social group. Priests are at one end of a defined spectrum of religious specialists; shamans are at the other. Societies create the religious specialists they use, and they don't use anthropological rules to tell them how to do it.
VanPool, Christine n.d. The signs of the sacred: Identifying shamans using archaeological evidence. Journal of Anthropological Archaeology in pressin press.