Matt. 10:1,40 - Jesus declares to His apostles, "he who receives you, receives Me, and he who rejects you, rejects Me and the One who sent Me." Jesus freely gives His authority to the apostles in order for them to effectively convert the world.
Matt. 16:19; 18:18 - the apostles are given Christ's authority to make visible decisions on earth that will be ratified in heaven. God raises up humanity in Christ by exalting his chosen leaders and endowing them with the authority and grace they need to bring about the conversion of all. Without a central authority in the Church, there would be chaos (as there is in Protestantism).
Luke 9:1; 10:19 - Jesus gives the apostles authority over the natural and the supernatural (diseases, demons, serpents, and scorpions).
Luke 10:16 - Jesus tells His apostles, "he who hears you, hears Me." When we hear the bishops' teaching on the faith, we hear Christ Himself.
Acts 1:15-26 - the first thing Peter does after Jesus ascends into heaven is implement apostolic succession. Matthias is ordained with full apostolic authority. Only the Catholic Church can demonstrate an unbroken apostolic lineage to the apostles in union with Peter through the sacrament of ordination and thereby claim to teach with Christ's own authority.
Acts 1:20 - a successor of Judas is chosen. The authority of his office (his "bishopric") is respected notwithstanding his egregious sin. The necessity to have apostolic succession in order for the Church to survive was understood by all. God never said, "I'll give you leaders with authority for about 400 years, but after the Bible is compiled, you are all on your own."
Acts 1:22 - literally, "one must be ordained" to be a witness with us of His resurrection. Apostolic ordination is required in order to teach with Christ's authority.
Acts 6:6 - apostolic authority is transferred through the laying on of hands (ordination). This authority has transferred beyond the original twelve apostles as the Church has grown.
Acts 9:17-19 - even Paul, who was directly chosen by Christ, only becomes a minister after the laying on of hands by a bishop. This is a powerful proof-text for the necessity of sacramental ordination in order to be a legitimate successor of the apostles.
Acts 13:3 - apostolic authority is transferred through the laying on of hands (ordination). This authority must come from a Catholic bishop.
Acts 14:23 - the apostles and newly-ordained men appointed elders to have authority throughout the Church.
Acts 5:13 - the people acknowledged the apostles' special authority and did not dare take it upon themselves.
Acts 15:6,24; 16:4 - the teaching authority is granted to the apostles and their successors. This teaching authority must be traced to the original apostles, or the authority is not sanctioned by Christ.
Rom. 15:16 Paul says he is a minister of Christ Jesus to the Gentiles in the priestly service of the gospel of God, so that the offering of the Gentiles may be acceptable. This refers to the ministerial priesthood of the ordained which is distinguishable from the universal priesthood of the laity. Notice the Gentiles are the sacrifice and Paul does the offering.
1 Cor. 5:3-5; 16:22; 1 Tim. 1:20; Gal 1:8; Matt 18:17 these verses show the authority of the elders to excommunicate / anathemize ("deliver to satan").
2 Cor. 2:17 - Paul says the elders are not just random peddlers of God's word. They are actually commissioned by God. It is not self-appointed authority.
2 Cor. 3:6 Paul says that certain men have been qualified by God to be ministers of a New Covenant. This refers to the ministerial priesthood of Christ handed down the ages through sacramental ordination.
2 Cor. 5:20 - Paul says we are "ambassadors" for Christ. This means that the apostles and their successors share an actual participation in Christ's mission, which includes healing, forgiving sins, and confecting the sacraments.
2 Cor. 10:6 in reference to the ordained, Paul says that they are ready to punish every disobedience. The Church has the authority excommunicate those who disobey her.