Jacob,
The New Testament is pretty clear that Jesus is the High Priest of a different and superior Priesthood than that of Aaron. If the Old Covenant and Priesthood were sufficient, then there would have been no need for a New Covenant and Priesthood.
Hebrews 8:1-7 Now the main point in what has been said is this: we have such a high priest, who has taken His seat at the right hand of the throne of the Majesty in the heavens, 2 a minister [a]in the sanctuary and in the true [c]tabernacle, which the Lord pitched, not man. 3 For every high priest is appointed to offer both gifts and sacrifices; so it is necessary that this high priest also have something to offer. 4 Now if He were on earth, He would not be a priest at all, since there are those who offer the gifts according to the Law; 5 who serve a copy and shadow of the heavenly things, just as Moses [d]was warned by God when he was about to erect the [e]tabernacle; for, “See,” He says, “that you make all things according to the pattern which was shown you on the mountain.” 6 But now He has obtained a more excellent ministry, by as much as He is also the mediator of a better covenant, which has been enacted on better promises. For if that first covenant had been faultless, there would have been no occasion sought for a second.
Hebrews 9:11-15 But when Christ appeared as a high priest of the good things [k]to come, He entered through the greater and more perfect [l]tabernacle, not made with hands, that is to say, not of this creation; 12 and not through the blood of goats and calves, but through His own blood, He entered the holy place once for all, [m]having obtained eternal redemption. 13 For if the blood of goats and bulls and the ashes of a heifer sprinkling those who have been defiled sanctify for the [n]cleansing of the flesh, 14 how much more will the blood of Christ, who through [o]the eternal Spirit offered Himself without blemish to God, cleanse [p]your conscience from dead works to serve the living God?
15 For this reason He is the mediator of a new covenant, so that, since a death has taken place for the redemption of the transgressions that were committed under the first covenant, those who have been called may receive the promise of the eternal inheritance.
