It is not an exaggeration to say that in order to understand this section of To the Hebrews it is imperative that one first understand the rituals of Yom Kippur (aka "The Day of Atonement"). These rituals are described in Leviticus 16. If you are not familiar with this passage I urge you to close up To the Hebrews and take the time to ponder that chapter. Far too many people cite snippets from To the Hebrews to "prove" things without understanding to what they actually refer. Here's a synopsis: http://jewishencyclopedia.com/articles/15117-yom-kippur
Hebrews 9 relates to the first ritual of this holy day, the day that the Israelites obtained forgiveness of sins. I say "obtained" because since the destruction of the temple in 70 CE these rituals are no longer observed. In this ritual the high priest (Aaron, a Levite) was to offer a bull (a male ox) by shedding his blood and sprinkling it before the lord as an atonement for himself, to express his remorse for his sins and for the sins of the people and to seek permission to proceed into the holy place and perform his priestly duty. This had to be done every year because rain or shine, every single year the priest had been beset with moral failings and was unfit to serve.
Heb 9:7 But only the high priest went into the second part, and then
only once a year, and never without blood, which he offered for
himself and for the sins committed by the people in ignorance.
So since Jesus is now the high priest, does he also need to perform this preparatory ritual each year? Does he have to offer a bull to apologize for sinning that year? No. Because Jesus did not approach God on the basis of the blood of a bull or goat but on the basis of his own blood being shed. In dying he became free from sin and death once and for all:
Heb 10:11 Day after day [annually] every [high] priest stands and
repeatedly offers the same sacrifices that can never take away [his]
sins [from his life]. Heb 10:12 But when this [high] priest [Jesus]
had offered for all time one sacrifice for [his sins and the people's]
sins, "he sat down at the right hand of God."
By dying to sin Jesus became forever free from sin and death and could serve perpetually, unlike the Aaronic priests:
Rom 6:7 For the person who has died has been freed from sin. Rom 6:8
Now if we have died with the Messiah, we believe that we will also
live with him, Rom 6:9 for we know that the Messiah, who was raised
from the dead, will never die again; death no longer has mastery over
him. Rom 6:10 For when he [Jesus] died, he died once and for all
to sin. But now that he is alive, he lives for God.
So, unlike Aaron and his sons, this high priest only had to die a single time because "death is permanent":
Heb 9:25 Nor did he go into heaven to sacrifice himself again and
again, the way the high priest goes into the Holy Place every year on
the basis of blood that is not his own. Heb 9:26 Then he would have
had to suffer repeatedly since the creation of the world. But now, at
the end of the ages, he has appeared once for all to remove sin by his
sacrifice. Heb 9:27 Indeed, just as people are destined to die once
and after that to be judged, Heb 9:28 so the Messiah presented
himself once [to serve God as chief priest] to carry away the sins of
many people. And he will appear a second time, not to deal with [his
own] sin, but to bring salvation to those who eagerly wait for him.
So in summary, unlike the offerings of the Aaronic priests which were required annually because of their sins, Jesus actually died to sin and since death is permanent so his freedeom from sin, and from death is permanent. So he's alive forever, free from sin and carrying away people's sins like the goat that carried off the sins of the Jews into the wilderness:
Lev_16:21 And Aaron shall lay both his hands upon the head of the
live goat, and confess over him all the iniquities of the children of
Israel, and all their transgressions in all their sins, putting them
upon the head of the goat, and shall send him away by the hand of a
fit man into the wilderness:
Heb 7:23 There have been many priests, since each one of them had to
stop serving in office when he died. Heb 7:24 But because Jesus
lives forever, he has a permanent priesthood. Heb 7:25 Therefore,
because he always lives to intercede for them, he is able to save
completely those who come to God through him. Heb 7:26 We need such
a high priest—one who is holy, innocent, pure, set apart from sinners,
exalted above the heavens. Heb 7:27 He has no need to offer
sacrifices every [yearly] day [of atonement] like high priests do,
first for his own sins and then for those of the people, since he did
this once for all when he sacrificed himself. Heb 7:28 For the Law
appoints as high priests men who are weak, but the promised oath,
which came after the Law, results in a Son who is eternally perfect.