The New Testament does talk about the ministry of prophetic speech and yet in many non-charismatic/non-Pentecostal churches, we don't tend to use "prophetic" as an adjective. It seems in the debate about spiritual gifts and ongoing revelation that it is too easy to simply abandon the use of a word or concept because we think it has been wrongly used by others. So... what do we do with the fact that the New Testament letters seem to talk about prophecy as a gift and even prophecies as something that should not be despised?
In the Scriptures we should first see that prophecy can denote both foretelling and forthtelling. If you were to survey the Scriptures, you would see that the most common form of prophetic ministry was the forthtelling of the truth of God applied to the audience. Sometimes it came through encouragement, sometimes through serious warning and calling God's people to his truth. At other times we do see prophets foretelling according to the promise of God to bring a Messiah and save his people and restore his creation.
In the New Testament, Paul tells the Ephesians that prophets were among the word-based ministries that God had graciously given to the church. Eph 4:11-12 And he gave the apostles, the prophets, the evangelists, the shepherds and teachers, 12 to equip the saints for the work of ministry, for building up the body of Christ. As far as the office of apostles and prophets are concerned, Paul had already told us that apostles and prophets were given as a foundational platform for the ministry of the church. Ephesians 2:19-20 So then you are no longer strangers and aliens, but you are fellow citizens with the saints and members of the household of God, 20 built on the foundation of the apostles and prophets, Christ Jesus himself being the cornerstone. This then suggests that out of the word-based ministry of the church, the apostles and prophets were the foundation on which the evangelists, shepherds and teachers would build as the church continued to grow upon that foundation. (It should be noted that many also believe that "prophets" in Ephesians 2:20 are a reference to Old Testament prophets).
Whatever the ministry of the prophets exactly was during the birth of the New Testament church, we can be sure that the direct inerrant revelation that formed the ministry of the apostles and prophets is now finally contained in the canon of the New Testament Scriptures. We still have the foundation of their ministry in the word of God.
What we can be sure about is that prophecies in the church were always meant for the edification of the church. They were to strengthen the church in their faith in Christ. Those who claim prophetic gifting and seek to tell me that I should paint my kitchen green have missed the point. 1 Corinthians 14:12 So with yourselves, since you are eager for manifestations of the Spirit, strive to excel in building up the church. 1 Corinthians 14:26 What then, brothers? When you come together, each one has a hymn, a lesson, a revelation, a tongue, or an interpretation. Let all things be done for building up.
1 Corinthians 14:29-32 Let two or three prophets speak, and let the others weigh what is said. 30 If a revelation is made to another sitting there, let the first be silent. 31 For you can all prophesy one by one, so that all may learn and all be encouraged, 32 and the spirits of prophets are subject to prophets. The word 'prophecy' and 'revelation' are used in this text synonymously and the point is that the speech seems to come from a true understanding of truth and is weighed carefully by those listening. It is spoken for the sake of the edification of the body. There is no indication here that this is direct revelation from God in addition to the inspired apostolic teaching in Christ. It is however weighed according to that apostolic teaching and the rest of Scripture.
All of this is to say that while there may no longer be inspired apostles and prophets in the church, the ministry of prophecy remains as the church teaches, counsels, corrects, warns, and instructs from the bible. The prophetic word is alive and well in the church whenever we open the Scriptures and minister with them. The whole church is a prophetic ministry to each other and the world. The ministry of the word is always primarily for the building up of the body of Christ.