A careful study of the Bible would confirm that while there may be succession of apostolic doctrine and apostolic ministry, nevertheless, there is no succession of apostolic office for the Church. Lest some people accuse me of prejudice against the so-called New Apostolic Reformation (NAR), I quote from the excellent position paper given by The General Council of the Assemblies of God (USA), “Apostles and Prophets”:
It is also clear that while the apostles (with the elders) were established leaders in the Early Church, there was no provision for their replacement or continuation…It is instructive, however, that nowhere in the New Testament after the replacement of Judas is any attention given to a so-called apostolic succession…It seems strange that apostles of Jesus Christ, concerned about faithful preservation of their message (cf. 2 Timothy 2:2), would provide for the appointment of overseers/elders while ignoring their own succession if such were indeed to be maintained.
In fact, there are certain exegetical hints the apostles of Jesus Christ are not to have successors. In 1 Corinthians 15:8, Paul listed all the Resurrection and post-Resurrection appearances of Christ and noted “last of all he appeared to me.” While some disagree, the statement is most commonly understood to mean Paul looked upon himself as the last apostle to whom Christ appeared.11 If this is the correct understanding, only the Twelve whom Jesus personally called and those He commissioned in His post-Resurrection appearances made up His original apostles…It is difficult to escape the conclusion of Dietrich Müller: “One thing is certain. The N[ew] T[estament] never betrays any understanding of the apostolate as an institutionalized church office, capable of being passed on…
Since the New Testament does not provide guidance for the appointment of future apostles, such contemporary offices are not essential to the health and growth of the church, nor its apostolic nature