'Perfection' in the Bible

But that that fell where the thorns were, these are they who having heard go away and are choked under cares and riches and pleasures of life, and bring no fruit to perfection.

If indeed then perfection were by the Levitical priesthood, for the people had their law given to them in connexion with it, what need was there still that a different priest should arise according to the order of Melchisedec, and not be named after the order of Aaron?