It's really hard not to read this part of a servant song in Isaiah as an image of Christ. In it's original context in Judah's exile, the servant in this poetic language could have been a metaphor for the whole nation: "When you make his life a sin offering, he will see his offspring and prolong his days," might be saying "We admit we were wrong and we have suffered your punishment, O God, and therefore we have hope that we will continue to be your people." It might be that the servant is one among the nation. "The righteous one, my servant, shall make many righteous." Makes me think of Abraham negotiating for the cities of Sodom and Gomorrah: "Suppose there are fifty righteous in the city," asks Abraham. "If I find at Sodom fifty righteous in the city, I will forgive the whole place for their sake," replies the Lord. If this one servant in Isaiah is righteous, then the whole nation can be forgiven and made righteous.
I think of the Christian admonition to pray for our enemies when Isaiah says the servant "made intercessions for the transgressors." But that's kinda different in some ways. When we pray for our enemies, there's a "them" that we're praying for. In the case of Isaiah, the servant is among "us" and praying for those among us who are transgressors. This is a beautiful antidote to the horrible political divide in our times. "Pray for your enemies," preserves the divide and keeps "them" in the group that has done wrong. "Pray for those among us who are transgressors," breaks down the divide. There's no "them" anymore. It admits the "we" can be the one who do wrong.
The bulk of this passage in Hebrews is about the subjecting of all things under the feet of humans. The author of Hebrews quotes Psalm 8, "subjecting all thing sunder their feet." but then says, "we do not yet see everything in subjection to them." it is empty praise of humans in general to say that all things are subjected under their feet, and then to feel so helpless both as individuals and as a society. The Author of Hebrews interprets this as not being about humans in general, but about one human in particular, Jesus. "but we do see Jesus . . . now crowned with glory and honor."
The one stands in for the many, as our reading in Isaiah was leading us, but this is different. In Isaiah, one from among "us" is righteous enough to pray for those among us who are transgressor. In the case of Hebrews, it's seems like there is no one among us who is righteous enough to do the intercessions. Jesus emptied himself, becoming one of us: "so that by the grace of God he might taste death for everyone," so that he could become the one among us who prays for us who are the transgressors. This is hugelly important to the book of Hebrews--it says in Hebrews 7:25, "he is able for all time to save those who approach God through him, since he always lives to make intercession for them."
So in Isaiah, we have a righteous servant among "us" who prays for those of us who are transgressors, and in Hebrews we have no such servant, but God becomes that servant for us in the person of Jesus Christ.