What did Jesus leave behind?

In response to my post Why is Jesus taking so long? the following query was made:

One question I have is what exactly Jesus came to accomplish---what did he establish that did not exist before?

I gave the first part of an answer in my post If the Messiah came, why do death and evil remain? It has something to with cosmology and the Holy Spirit. Bartholomew and Goheen, whose book The Drama of Scripture has provided the basis of these posts, give a further clarification to this answer, this time in terms of the church, "the people of God."

The church’s new life is based on what God has done in the death and resurrection of Jesus Christ. In Christ’s death, God has defeated the powers that rule “this present age”—sin, evil, and death. In Christ’s resurrection the “age to come” has begun, with its promise of life, love, and peace (Romans 6:1–11). The church’s new life is also empowered by the Spirit, which lives within the community of believers and constantly brings new life to it (Romans 8; Galatians 5). This, says Paul, is the new life of the Christian, begun by Christ’s work on the cross, lived out in the Father’s kingdom, and shaped by the Spirit’s power.

At the heart of this new life is a new relationship to God, which Paul describes in terms of righteousness, reconciliation, and adoption. First, since God is the righteous Lawgiver and Judge, we who follow rebellious Adam are estranged from him by our sin; we too are guilty. But Paul proclaims the good news that (for those who have faith in Jesus) our “guilty” verdict has been overturned. There is a new verdict: we have already been declared righteous—on the basis of the death of Jesus Christ (Romans 3:21–31; Galatians 2:15–16; 3:6–14).As far as the Christian is concerned, God’s final judgment has already taken place! With our guilt removed, we stand in a right relationship to God.

Second, since we were once estranged from God by our sinful rebellion, we need to be reconciled to him. Reconciliation, long thought to become available only at the end of time with the coming of God’s kingdom, is a gift freely offered even now (2 Corinthians 5:18–19; Colossians 1:20).Reconciliation removes the sin that has put God’s world p 193 at enmity with him and leads to peace. This means the restoration of the shalom and harmony of God’s original created order for the whole world and especially for humankind (Romans 5:1). Third, we who are born into the sinful race of Adam are restored to God by receiving his gift of adoption (Galatians 4:4–5; Ephesians 1:4). The same Spirit that lived in Jesus is poured into our own lives and enables us to call God “Abba, Father,” as Jesus did (Romans 8:14–15).

This is the church: a people who live in a new world with a new identity and a new relationship to God. Thus, Paul commands the church to live more and more the new life of God’s kingdom, to “take off” the old self (as if it were soiled clothing) and to put on the new (Ephesians 4:22–24; Colossians 3:9–10). In other words, they are to bid farewell to the way of life that was shaped by their experience of “this present age” and to embrace a new way of life as part of “the age to come.” And with this new life comes a call to a new kind of obedience to God’s law in every part of life, an obedience rooted in love.

Bartholomew, C. G., & Goheen, M. W. (2004). The drama of Scripture: Finding our place in the biblical story (192–193). Grand Rapids, MI: Baker Academic.