Hebrews 9:11-28: "11 But when Christ appeared as a high priest of the good things that have come, then through the greater and more perfect tent (not made with hands, that is, not of this creation) 12 he entered once for all into the holy places, not by means of the blood of goats and calves but by means of his own blood, thus securing an eternal redemption. 13 For if the blood of goats and bulls, and the sprinkling of defiled persons with the ashes of a heifer, sanctify for the purification of the flesh, 14 how much more will the blood of Christ, who through the eternal Spirit offered himself without blemish to God, purify our conscience from dead works to serve the living God.
"15 Therefore he is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance, since a death has occurred that redeems them from the transgressions committed under the first covenant. 16 For where a will is involved, the death of the one who made it must be established. 17 For a will takes effect only at death, since it is not in force as long as the one who made it is alive. 18 Therefore not even the first covenant was inaugurated without blood. 19 For when every commandment of the law had been declared by Moses to all the people, he took the blood of calves and goats, with water and scarlet wool and hyssop, and sprinkled both the book itself and all the people, 20 saying, 'This is the blood of the covenant that God commanded for you.' 21 And in the same way he sprinkled with the blood both the tent and all the vessels used in worship. 22 Indeed, under the law almost everything is purified with blood, and without the shedding of blood there is no forgiveness of sins.
"23 Thus it was necessary for the copies of the heavenly things to be purified with these rites, but the heavenly things themselves with better sacrifices than these. 24 For Christ has entered, not into holy places made with hands, which are copies of the true things, but into heaven itself, now to appear in the presence of God on our behalf. 25 Nor was it to offer himself repeatedly, as the high priest enters the holy places every year with blood not his own, 26 for then he would have had to suffer repeatedly since the foundation of the world. But as it is, he has appeared once for all at the end of the ages to put away sin by the sacrifice of himself. 27 And just as it is appointed for man to die once, and after that comes judgement, 28 so Christ, having been offered once to bear the sins of many, will appear a second time, not to deal with sin but to save those who are eagerly waiting for him."
Hebrews 10:10-22: "10 And by that will we have been sanctified through the offering of the body of Jesus Christ once for all.
"11 And every priest stands daily at his service, offering repeatedly the same sacrifices, which can never take away sins. 12 But when Christ had offered for all time a single sacrifice for sins, he sat down at the right hand of God, 13 waiting from that time until his enemies should be made a footstool for his feet. 14 For by a single offering he has perfected for all time those who are being sanctified.
"15 And the Holy Spirit also bears witness to us; for after saying, 16 'This is the covenant that I will make with them after those days, declares the Lord: I will put my laws on their hearts, and write them on their minds,' 17 then he adds, 'I will remember their sins and their lawless deeds no more.' 18 Where there is forgiveness of these, there is no longer any offering for sin.
"19 Therefore, brothers, since we have confidence to enter the holy places by the blood of Jesus, 20 by the new and living way that he opened for us through the curtain, that is, through his flesh, 21 and since we have a great priest over the house of God, 22 let us draw near with a true heart in full assurance of faith, with our hearts sprinkled clean from an evil conscience and our bodies washed with pure water."
Jeremiah 31:31-34: "31 'Behold, the days are coming, declares the LORD, when I will make a new covenant with the house of Israel and the house of Judah, 32 not like the covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt, my covenant that they broke, though I was their husband, declares the LORD. 33 But this is the covenant that I will make with the house of Israel after those days, declares the LORD: I will put my law within them, and I will write it on their hearts. And I will be their God, and they shall be my people. 34 And no longer shall each one teach his neighbor and each his brother, saying, "Know the LORD," for they shall all know me, from the least of them to the greatest, declares the LORD. For I will forgive their iniquity, and I will remember their sin no more.'"
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The texts from Hebrews are the main sources for the hymn. The beginning of the first verse ("No temple now, no gift of price, / No priestly round of sacrifice, / Retain their ancient pow'rs.") comes from 9:11-14 and 10:11.
The second verse begins by describing Jesus' "One final full self-off'ring made, / Complete in ev'ry part," which is described in Hebrews 9:25-28 and 10:10, 14. The end of the verse refers to "The law within the heart," which is mentioned in Hebrews 10:16 and Jeremiah 31:33.
The third verse, specifically the lines "In faith and confidence draw near, / Within the holiest appear" and the description "One great imperishable Priest," comes from Hebrews 10:19-22.
The fourth verse extends from the third, but I don't think it draws from any of the cited texts.
The second verse begins by describing Jesus' "One final full self-off'ring made, / Complete in ev'ry part," which is described in Hebrews 9:25-28 and 10:10, 14. The end of the verse refers to "The law within the heart," which is mentioned in Hebrews 10:16 and Jeremiah 31:33.
The third verse, specifically the lines "In faith and confidence draw near, / Within the holiest appear" and the description "One great imperishable Priest," comes from Hebrews 10:19-22.
The fourth verse extends from the third, but I don't think it draws from any of the cited texts.