It Is A Perpetual Cycle

Paul professes confidence, concerned he may have offended the Romans.

14 My brothers and sisters, I myself am convinced about you that you also are full of goodness, filled with all knowledge, and able to instruct one another.

15 Nevertheless, I have written to remind you more boldly on some points because of the grace given me by God 16 to be a minister of the Messiah Jesus to the Gentiles, serving as a priest of the Good News of God. God’s purpose is that the Gentiles may be an acceptable offering, sanctified by the Holy Spirit. 17 Therefore I have reason to boast in Messiah Jesus regarding what pertains to God.
(Romans 15:14-17, Christian Standard Bible)

John Stott:

Although Paul's priestly ministry as apostle to the Gentiles was unique, the principle he enunciates has a vital contemporary application. All evangelists are priests, because they offer their converts to God. Indeed, it is this truth more than any other which effectively unites the church's two major roles of worship and witness.

It is when we worship God, glorying in his holy name, that we are driven out to proclaim his name to the world. And when through our witness people are brought to the Messiah, we then offer them to God. Further, they themselves join in his worship, until they too go out to witness.

Thus worship leads to witness, and witness to worship.
It is a perpetual cycle.

No wonder Paul is grateful for his share in this privileged ministry and breaks out: Therefore I glory in Messiah Jesus in my service to God (v17).