The answer depends largely on how we define “apostle” and “prophet.” The Twelve and Paul were apostles in a special sense. As men who had seen the risen Christ, making them eyewitnesses of the Resurrection, they were used inlaying the foundation of the New Testament Church. Obviously, no one today walked the dusty roads of Nazareth with Jesus, heard His voice, enjoyed meals with Him, or witnessed His crucifixion. The Twelve did all these things, and they met with and were instructed by Christ after His resurrection. The word “apostle,” as it applied to them, was a foundational office. It cannot be repeated, for the foundation has already been laid. So, in the sense in which the Twelve were apostles, there are no living apostles today. However, insofar as the word “apostle” merely refers to a person sent with a message or on a mission, whether secular or religious, there may be many “apostles” today.

The term “prophet” also has more than one nuance of meaning. There were prophets who received direct revelation from God. In fact, in that sense, some of the apostles were prophets. This function, too, was foundational for the New Testament church. Paul had in view apostles and prophets as foundational offices/functions when he wrote:

“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, in whom the whole building, being fitted together, grows into a holy temple in the Lord” (Ephesians 2:19–21).

So in the foundational sense, there are no prophets today. But not all prophets in the New Testament church contributed to the original deposit of faith. Some prophets, such as the disciples Paul met in Tyre (Acts 21:4), the four virgin daughters of Philip (verse 9), and Agabus (verse 10), prophesied of events to come, but they apparently added nothing to the deposit of “the faith which was once for all delivered to the saints” (Jude 3). The true Faith, in its pristine purity and fullness, had already been “delivered to the saints” by the time these prophets came on the scene. So they were not prophets in the foundational sense.

Are there Agabus-like prophets today? I don’t know of any, but that doesn’t mean there are none. Revelation 11 seems to indicate God will use prophets before the close of the age. So does Acts 2:17–18 (RSV):

“And in the last days it shall be, God declares, that I will pour out my Spirit upon all flesh, and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams; yea, and on my menservants and my maidservants in those days I will pour out my Spirit; and they shall prophesy” (see also Joel 2:28).

It is entirely possible that God has used prophets at various times in the past two millennia, is using them in certain places today, and will use them in the days ahead. But it’s important to understand that none of these have added, or will add, new revelation to the true Faith that was once for all delivered to the saints.

The word “prophet” can also refer to an inspired preacher. The “prophet,” in this sense, is inspired of the Holy Spirit, but his inspired preaching does not necessarily involve foretelling future events; nor does it involve divine disclosures apart from what is already revealed in Scripture. Rather, it involves the ability to comprehend Scripture and expound its message clearly. Paul seems to have this sense of “prophesying” in mind in 1 Corinthians 14:3: “But he who prophesies speaks edification and exhortation and comfort to men.”