I'm not sure what you mean by "like the OT priests", but there is biblical justification for Priests after the Gospels:
But you are a chosen race, a royal priesthood, a holy nation, a people for his own possession, that you may proclaim the excellencies of him who called you out of darkness into his marvelous light.
1 Peter 2:9
Also the Bible calls Jesus the high priest, not the only priest.