Excuse me, but the English word "priest" comes directly from the Greek word presbyter (elder), and the office of elder was most certainly not "made obsolete along with the Old Covenant". In fact, it was instituted as part of the New Covenant.
A priest intercedes between man and God, while bishops oversee a church.
All Christians are called to intercede for each other.
A bishop is an episkopos or overseer. The office presbyter, during or shortly after NT times, became the deputy or vicar of the bishop, as bishops were understood to oversee the entire church of a small region or city. This is crystal clear from the writings of Ignatius of Antioch (d. AD 107), who knew the Apostles personally.
And, BTW, the NT says that we are all priests, in the sense of a different Greek word, hieratos, one who offers sacrificial worship to a deity.
Thanks for making my point. Contrast that with the Catholics’ practice and you’ll see another of their many disputes with Scripture.