Hebrews 7:12

For the priesthood being changed, there is made of necessity a change also of the law.

The Aaronic priesthood gives way to a greater priesthood, and with that change the order of priestly service is lifted to a higher plane. Consecration for this service comes through grace and through the righteousness of Christ received by the believer. Those thus consecrated and filled with the Holy Spirit become part of a royal priesthood. In that priesthood they represent Christ, ministering in His spirit and by His power rather than by earthly lineage.