Hebrews 7:28

For the law appointeth men high priests, having infirmity; but the word of the oath, which was after the law, appointed a Son, perfected forevermore.

It is still paramount in the author's mind that the oath by which God swore to bring in a Messiah Priest after the order of Melchizedek came such a long, long time after the law had been in operation; thus he reiterates here, "which was after the law." It is the vast implications of this which he has just been discussing at such length. The verse is a recapitulation of what had already been said - that the Levitical priests were weak, mortal, sinful people; but that the Son of God, the glorious priest forever after the order of Melchizedek is perfected forevermore.