There is no "NAR" per-se. The term is derived from a quote from a charismatic Christian named C. Peter Wagner. The term "New Apostolic Reformation," primarily, has been used by detractors who don't agree with the theology of people who among those who are connected, loosely or otherwise, with C. Peter Wagner and others. In order to use broad, sweeping terms against these people, the term has been thrown around a great deal (especially on the internet).
One clear group who has a problem with the so-called "NAR" would be anyone who believes the Spiritual gifts have ceased. Additionally, there are charismatics who believe in the moving of the Spiritual gifts, but refuse to recognize the 5 fold ministry giftings today.
Moreover, they don't really understand the 5 fold ministry. The ministries are not "Spiritual" gifts, they are different. It's basically a powerful manifestation of Jesus in one or more of the 5 fold ministries that He walked out when He was on the earth.
For example, Jesus will put something of a supernatural element within those whom He has chosen to walk out leadership ministry callings. What basically happens is Jesus "gifts" the Body of Christ with a person whom He uses in very powerful ways to lead the Body, and equip and train others.
Billy Graham, for instance, was an evangelistic gift to the Body. God saw his humble man surrender and so He chose to put something no man can boast about within Him in a supernatural manifestation of Jesus working as an evangelist through Him. When Billy Graham preached the gospel, it was Jesus the evangelist working through Him, which is why his ministry was so effective.
Another beef detractors have is that they claim apostles are no longer walking the earth. This is kind of silly, as apostles are given a supernatural manifestation of Christ to to two things: Establish things for the Kingdom of God, and train and equip other leaders.
Consider Paul's evangelistic efforts to establish the church in Asia Minor. Consider his letters to Timoty and Titus to train them to be leaders in the church. Paul was functioning in that apostolic gifting.
The truth is, these giftings have been active since Jesus began to give gifts when He ascended on high. Look down the ages at men of God and how Jesus used them. Surely, Martin Luther was a prophetic, apostolic gift to the Body, as he was used to call out the failing established church from its error (as a prophet) and then establish (as an apostle) a new, reformed order that would allow God's people to thrive and get back on track with Him.
Look at all the powerful movements of God down the last 2,000 years. Each one had leaders who stood out with one or more of the 5 fold ministry giftings.
Hudson Taylor, Count Zinzendorf, Richard Wurmbrand, Calvin, Martin Luther, Billy Graham, John Wesley, etc, etc, etc... I could go on.
If we look at any of these ministries, we would clearly see one or more 5 fold ministry gift at work, and that's to the praise and glory of God because the gift, in fact, is Jesus manifesting through mankind to establish, build, and expand His Kingdom on earth.
Jesus said, "I will build My church." And He wasn't kidding...