Matthew Poole and continuators on Hebrews 7:21

21 (For those Priests were made without an oath : but this with an oath, by him that said unto him, The Lord sware , and will not repent, Thou art a priest for ever after the order of Melchisedec.)

Those Priests of Aaron's Order were selected, instituted, consecrated without any Oath mentioned by Moses, who did all exactly as the Lord commanded him, Exod. 40.16. God gave only command for it, and made their Priesthood but a temporary and passing Honour and Office, which he might alter when he would:

But he, or Iesus, was made a Priest after Melchisedec's Order, by an Oath of God his Father, speaking to him, as is recorded by David, Psalm 110.4. The Lord Iehovah the Father, sware unto his Son the Lord Messiah, lifting his Hand, and saying, I live for ever, Deut. 32.40. when he ascended and sate down on the Right Hand of the Majesty in the Heavens, solemnly by this Oath ratifying and confirming him in this Office, and that he would not repent, i. e. change, or alter, or retract what he swore to him, there being no need of any other, he so effectually performing the work of it, that all that God bestows upon his by him, are Gifts not to be repented of, even eternal Life and Salvation. That which the Oath ratified, was, That Christ should be God's only and eternal Priest, who was to have no Sharer with him in the Priesthood, and no end of it; taking away from himself by Oath any power to make Christ no Priest, or take away his Office at will and pleasure, as he did Aaron's; hereby honouring his Son, and highly gratifying Sinners by giving them such a Royal High-Priest, who should effectually manage all their Concernments with him for ever.

Marginal references: Or, Without swearing of an Oath.