'Perfection' in the Bible

Wherefore, having left the word of the beginning of the Christ, unto the perfection we may advance, not again a foundation laying of reformation from dead works, and of faith on God,

If indeed, then, perfection were through the Levitical priesthood -- for the people under it had received law -- what further need, according to the order of Melchisedek, for another priest to arise, and not to be called according to the order of Aaron?