In Christ, the church exists for mission

Trinitarian theology (with its doctrine of God) is the basis for a Trinitarian ecclesiology (with its doctrine of the church) and a Trinitarian missiology (with its doctrine of the church's participation in the mission of the triune God).

For an in-depth look at all three, I recommend Incarnation: The Person and Life of Christ, and Atonement: The Person and Work of ChristBoth books contain the lectures of T.F. Torrance as edited by Robert T. Walker.

Chapter 11 of Atonement sets out Torrance's Trinitarian ecclesiology. He notes that the church, "formed in history as God called and entered into communion with his people," has three historical forms:
  1. A preparatory form before the incarnation (beginning with Adam and focusing on Israel under the old covenant).
  2. A new form in Jesus, through the Spirit (the present church under the new covenant).
  3. A final and eternal form in the new creation ushered in at Jesus' coming in glory (p. 342ff).
The church in its present form (#2), is the church given new birth as the New Israel of God, in Jesus' resurrection and the outpouring of the Holy Spirit at Pentecost (p. 353). It is "the one body of Christ incorporating the faithful of all ages before and after the incarnation" (p. 354). Moreover, it is "the communion of saints, the whole company of the redeemed in heaven and earth, living in communion with God through the Holy Spirit...all who are baptized in the name of the Father, the Son and the Holy Spirit and live in faith and obedience to him" (pp. 361-362).

Did Jesus begin the church? Torrance answers: "The records make it clear that Jesus intended to leave behind a community with a structure and form and leadership, a community with a ministry shaped on the pattern of his own" (p. 356).

Trinitarian missiology
What is the purpose that Jesus gave to his body, the New Testament church? Torrance answers: "It is quickened and born of the Spirit...filled and directed by the order that the church may be rooted in Jesus Christ, grounded in his incarnate being and order that it may be determined in its inner and outer life through participation in [Jesus'] life and ministry" (p. 355).

Furthermore, the church is "the community of men and women filled with the presence of the Spirit, partaking of the...fullness of the blessings and riches of God, and therefore sent out in the power of the Spirit to live out the divine life and love among humankind as the bodily instrument and image of Christ in the world and the one comprehensive communion of the Spirit" (p. 361).

In short, the church exists in Christ for mission to the world. It is not, merely that the church has a mission, but that the church exists for mission - ecclesiology and missiology, in Christ, are inseparably linked and grounded in the person and work of Jesus.

In this mission, the church is "both like and unlike the ministry of the historical Jesus. It is rooted in it and patterned after it, and in a real sense shares in it. But it is a ministry of redeemed sinners, whereas [Jesus'] ministry is that of the redeemer" (p. 357). As the company of Jesus' disciples in the world, the church is sent in the Holy Spirit to the world, participating in the ministry that Jesus is now doing there to fulfill the Father's mission to call all people from union to communion with God.

The church does this work by both being and proclaiming the good news (the gospel) to the world. We see this purpose unfolding in Jesus' sending of his first disciples. According to Torrance, "the disciples were permitted to baptize, to go forth as [Jesus'] representatives bearing the [proclamation] of the kingdom on their lips and with authority to heal and forgive sins in his name" (p. 355).

Indeed, the church, Jesus, and Jesus' mission are inseparably linked: "The being and nature of the church are equally inseparable from its mission, that is, its sending by Christ on the mission of the love of God, just as the sending of Christ by the Father is inseparable from his being and nature as the incarnate Son" (p. 373).

Through the work of Jesus, in the Spirit, within the church, the church "becomes itself a communion of love through which the life of God flows out in love toward every human being. As he is, so are we in this world" [Phil 2:1-8] (p. 375).