This is a great video on the NAR. Something that really jumped out at me is something Russ Moyer says. Moyer is the "Presiding Prophet" of the
International Coalition of Apostolic Leaders. The part I'm talking about starts at 35:25. He says:
". . .apostles and prophets walking together, re-laying the foundation of Ephesians 2:18-20."
I don't know, it seems to me this should be a red alert to any Bible-believing Christian. Here's what Ephesians 2:18-20 says:
"For through Him we both have access by one Spirit to the Father. Now, therefore, you are no longer strangers and foreigners, but fellow citizens with the saints and members of the household of God, having been built on the foundation of the apostles and prophets, Jesus Christ Himself being the chief cornerstone,"
I don't know what part of "having been built" Moyer doesn't understand, or where he thinks he got the mandate to "re-lay" the foundation that's already been laid. The Greek ἐποικοδομηθέντες (epoikodomēthentes) is aorist participle, meaning an action that took place in the past. If it was an action that took place in the past but continuously over a long period, the Imperfect tense would have been used.
If the author is referring to past apostles and prophets, referring to the past does not mean that he is making commentary about the present or the future. The ministry of apostles and prophets was an ongoing thing when he wrote this. There were also historical prophets and some commentators think this might refer to the Biblical prophets, others his contemporaries. But saying the church has been built on apostles and prophets is not a commentary on whether God would continue to place these roles in the church. Reading such an idea into the text there is eisegesis.
Consider this passage
Ephesians 4
8 Wherefore he saith, When he ascended up on high, he led captivity captive, and gave gifts unto men.
9 (Now that he ascended, what is it but that he also descended first into the lower parts of the earth?
10 He that descended is the same also that ascended up far above all heavens, that he might fill all things.)
11 And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers;
The gifts were given at the ascension, but people started operating them, in some cases, later. It took some time before Philip the evangelist went down to Samaria to preach. Paul's conversion and sending as an apostle was not instant at the ascension of Christ. Most Christians would acknowledge some ministry in the list. For example, most Christians--- or leaders from their churches--- would acknowledge that there are still pastors and teachers. Many Christians acknowledge the role of evangelists.
Individual Christians are not allowed to create a doctrine that these gifts of Christ will not manifest in the church. It is not up to us to declare what Christ does or does not decide. We can hope, through discernment, wisdom, and through the Holy Spirit to perceive what the Spirit is doing. The apostles and elders in Jerusalem were able to agree on what 'seemed good to the Holy Spirit.'
The prophets and teachers in Antioch were able to perceive the Spirit speaking to them to separate Barnabas and Saul to the work to which he had called them in Acts 13. They went forth, being sent by the Spirit. After this, Acts calls both Barnabas and Saul "apostles" for the very first time. Compare this to Christ sending forth the twelve apostles. Their being named 'apostles' comes before their being sent on a journey in which they were to heal, cleanse lepers, and raise the dead and preach in one Gospel, and another Gospel calls them 'apostles' for the first time after they returned.
Acts 14:4 and 4:14 call Barnabas and Saul (a.k.a. Paul) 'apostles'). Paul mentions Barnabas again in I Corinthians 9 in the discussion of his own right as an apostle to live of the Gospel, which makes sense in the light of Barnabas being an apostle also. I Thessalonians 1:1 shows the epistle is written by Paul, Silvanus, and Timothy. In 2:6-7 we see them using the term 'apostles of Christ' to describe themselves. Paul seems to include Apollos also in his discussion of 'we apostles' in I Corinthians 3.
Saying that God will not send an apostle today is tantamount to saying how God will run His church. When He has not revealed something, we should not decree what He will and will not do. But through God's grace, the saints can be enabled to discern the working and will of the Spirit.
Historically, there have been many individuals the Christian community has recognized as apostles, at least looking back on them in history. The term is used of men who did missions work, especially if they were influential in introducing the Gospel to a people-group or converting many of them. As Roman Catholicism does today, there was a bit of a trend to associate apostolic authority with bishops or with roles up the RCC hierarchy. and some of the men labeled 'apostles' were ordained as bishops.
Examples of men historically called apostles include Patrick of Ireland. There are also writings about the 'twelve apostles of Ireland' but I think it was unlikely that all were bishops. Columba had that title, and he was known for reaching the Picts in Scotland. There is Oscar/Angsar 'apostle of the north.' Cyril and Methodius were two brothers who are known as the 'Apostles to the Slavs' and Bulgars-- actually to a long list of groups.
In Protestantism, John Elliot is known as 'Apostle to the Indians' in colonial America. I saw a Congregational hymn about workers, probably missionaries, that says, "Make them apostles..." The concept does exist in Protestant tradition. I also recollect that one of Calvin's commentaries also leaves it open for God to send apostles and prophets to the church, and he may have believed there were some in his own time.
I take issue with some of the NAR views of apostleship-- the idea that it is a hierarchical role that is supposed to be set above local church eldership. Paul's and his co-workers measure of rule extended to the areas where they had brought the Gospel of Christ. Paul accepted James and the elder's advice when he went to Jerusalem. There is no hint that he tried to pull 'apostolic rank' over the elders. I once emailed Peter Wagner an article on this topic, but he responded asking not to receive any further emails of this kind. I did not know him, so that was also understandable.