But when Christ appeared as a High Priest of the good things to come [that is, true spiritual worship], He entered through the greater and more perfect tabernacle, not made with hands, that is to say, not a part of this [material] creation. He went once for all into the Holy Place [the Holy of Holies of heaven, into the presence of God], and not through the blood of goats and calves, but through His own blood, having obtained and secured eternal redemption [that is, the salvation of all who personally believe in Him as Savior]. For if the sprinkling of [ceremonially] defiled persons with the blood of goats and bulls and the ashes of a [burnt] heifer is sufficient for the cleansing of the body, how much more will the blood of Christ, who through the eternal [Holy] Spirit willingly offered Himself unblemished [that is, without moral or spiritual imperfection as a sacrifice] to God, cleanse your conscience from dead works and lifeless observances to serve the ever living God? – Hebrews 9:11-14
Observe the three members of the Trinity in this passage — Father, Son and Holy Spirit — is involved.
The voluntary nature of the offering gives it especial efficacy. He “through the eternal Spirit,” that is, His divine Spirit (Ro 1:4, in contrast to His “flesh,” Heb 9:3; His Godhead, 1Ti 3:16; 1Pe 3:18), “His inner personality” [Alford], which gave a free consent to the act, offered Himself. The animals offered had no spirit or will to consent in the act of sacrifice; they were offered according to the law; they had a life neither enduring, nor of any intrinsic efficacy. But He from eternity, with His divine and everlasting Spirit, concurred with the Father’s will of redemption by Him. His offering began on the altar of the cross, and was completed in His entering the holiest place with His blood. The eternity and infinitude of His divine Spirit (compare Heb 7:16) gives eternal (“eternal redemption,” Heb 9:12, also compare Heb 9:15) and infinite merit to His offering, so that not even the infinite justice of God has any exception to take against it. It was “through His most burning love, flowing from His eternal Spirit,” that He offered Himself [Oecolampadius]. – Jamieson-Fausset-Brown
Who through the eternal Spirit – The work of redemption being the work of the whole Trinity. Neither is the Second Person alone concerned even in the amazing condescension that was needful to complete it. The Father delivers up the kingdom to the Son; and the Holy Ghost becomes the gift of the Messiah, being, as it were, sent according to his good pleasure. Offered himself – Infinitely more precious than any created victim, and that without spot to God. Purge our conscience – Our inmost soul. From dead works – From all the inward and outward works of the devil, which spring from spiritual death in the soul, and lead to death everlasting. To serve the living God – In the life of faith, in perfect love and spotless holiness. – Wesley
As Christ’s miraculous conception was by the Holy Spirit, and he wrought all his miracles by the Spirit of God, so his death or final offering was made through or by the eternal Spirit; and by that Spirit he was raised from the dead, 1 Peter 3:18. Indeed, through the whole of his life be was justified by the Spirit; and we find that in this great work of human redemption, the Father, the Son, and the Holy Spirit were continually employed. – Adam Clarke