Caiaphas was High Priest during all of Jesus ministry, holding office between 18–36 ad. Jesus’ ministry is usually said to cover the years 30–33 ad.
Caiaphas conducted the next phase of Jesus’ trial. He had more spiritual authority than Annas, so he was able to precipitate the crisis during Jesus’ trial that could achieve the verdict he wanted. Three passages: Matthew 26:3,4, Matthew 26:63–66 and John 11:49-53 describe this aspect of the trial.
Annas and Caiaphas next appear after Jesus’ death, resurrection, and ascension. Acts 4:6,7 describes them interrogating Peter and John about a miracle they performed.
There is one further fascinating footnote to the story. Caiaphas is the only person mentioned in the Bible for whom we have proven physical remains. In November 1990, workers constructing a water park south of the Old City of Jerusalem accidentally uncovered a small burial cave containing twelve limestone mortuary chests. These types of chests were known as ‘ossuaries’ and used in the first century ad. In one chest were the bones of a man who died at an age of about sixty. The style and lavish carving point to a High Priest, and the lettering suggests a man whose name was Caiaphas.