Not really. Pentecostalism doesn't recognize the
office of apostle. But they teach there are those who
function as apostles; especially evangelists who preach the gospel and perform "signs and wonders."
The NAR has mostly grown out of Pentecostalism and other charismatic groups, but they're not officially affiliated with any of them. They're loosely affiliated groups who teach and preach the same things: Mainly that the office of apostle has been restored and the model for churches needs to undergo a major shift. In other words, churches are to no longer be led by pastors but by an apostle. An apostle usually has many churches under his authority.
They claim to not be organized, but if the
International Coalition of Apostolic Leaders isn't an organization I don't know what is.