In what way is the saving work of Christ continued?
The saving work of Christ is continued in the Catholic Church, especially through the Seven Sacraments which He instituted. The Holy Spirit gives His grace through the sacraments and sanctifies souls.
By means of the gift of the Holy Spirit, the Catholic Church enjoys Christ’s presence and continues His ministry and saving mission.
Jesus promised to remain with us, through the Holy Spirit. He promised this the night before He died, “Nevertheless I tell you the truth: it is to your advantage that I go away, for if I do not go away, the Counselor will not come to you; but if I go, I will send him to you. And when he comes, he will convince the world of sin and of righteousness and of judgment: of sin, because they do not believe in me; of righteousness, because I go to the Father, and you will see me no more; of judgment, because the ruler of this world is judged.
I have yet many things to say to you, but you cannot bear them now. When the Spirit of truth comes, he will guide you into all the truth; for he will not speak on his own authority, but whatever he hears he will speak, and he will declare to you the things that are to come. He will glorify me, for he will take what is mine and declare it to you. All that the Father has is mine; therefore I said that he will take what is mine and declare it to you. A little while, and you will see me no more; again a little while, and you will see me.” (John 16:7–16).
Before ascending into Heaven, Jesus commanded His Apostles to teach all nations and to baptize: “Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit; teaching them to observe all that I have commanded you; and lo, I am with you always, to the close of the age” (Matthew 28:19–20).