There is no need for other sacrifices. The liturgy of the Last Supper, which we call the Mass, is a sacrifice in the sense that it makes present again for Christians of different times and places the possibility of participating in the Body and Blood of Christ in commemoration of him, proclaiming the death of the Lord until he comes. The Mass is in no way a separate sacrifice from the sacrifice of the cross. It is not a new sacrifice replacing the sacrifice of the cross or adding to it as if the sacrifice were insufficient. Jesus, the Catholic Church holds, is the one high priest of the new covenant.
Catholics refer to our clergy as priests.
That terminology recognizes that when a Christian, designated by ordination, presides at the Eucharist, which recalls the death of the Lord until he comes, that person represents Jesus the high priest and not merely the community. Our doctrine of the Mass as representing the one priestly sacrifice of Jesus is, in our judgment, fully biblical. Christ saves Christians in and through the Church. We believe that Christ is operative in the sacraments of the Church and that it is Christ who gives the grace that touches lives. That formula is meant to say that the efficacy of the sacraments is not dependent on the clergyperson or administrator of the sacrament.