There are many prophets described in the Bible. In the OT, and also in the NT:
Jesus was, among other things, a prophet, Joseph, Mary and Elizabeth received prophecy, Peter's dream, Paul's conversion, John's revelation, Pentecost... etc, etc.
What about today...
Is prophecy still an accepted aspect of the experience of some Christians?
Could it lead to valid beliefs that are not explicit in the existing scriptures?
It depends on what what means by "prophecy".
Do new prophets with new revelation(s) from God show up? No.
The New Testament does talk about the charism--"gift"--of prophecy as one of the gifts of the Spirit that are present in the life of the Church.
I come from the position that the gift of prophecy has nothing to do with ecstatic utterances, that would be a Montanist view of prophecy which is heretical. Likewise prophecy has nothing to do with imparting revelatory knowledge, nor with predicting the future. Rather prophecy is the gift of speaking God's word.
When it comes to prophets in the Christian sense I would point to someone like Martin Luther King, Jr. King's boldness to speak the truth of God in the midst of a hostile world, proclaiming truth to power, and calling the Church to repentance are examples of what the prophetic life Christianity ought to look like.
It's therefore not about being a "prophet", but rather the prophetic reality of the power of God's word to cut through to the heart of things. That prophetic voice in the Church calls the Church to faithfulness and repentance, and it speaks truth to power. That prophetic voice is wherever God's word is being preached, not just in more extraordinary individuals like Dr. King, but at every pulpit where God's word is proclaimed for our own hearing.
In that sense every ordained pastor exercises the gift of prophecy whenever they preach the word to the Faithful. In the same way, pastors exercise the apostolic gifts when they serve in their pastoral capacity: Such as in the words of Absolution, and in the consecration of the elements of the Eucharist. These things are subsumed into the ministry or office of the Keys.
And so the exercising of the prophetic and apostolic is found not in extraordinary ministers such as the calling of new "prophets" or new "apostles"; but in the proper and faithful exercising of the Keys in the life of the Church.
But, again, sometimes certain individuals do seem to have a unique calling and to serve in a certain way at that time and place--such as Dr. King as already mentioned. I think Luther also served an important purpose for this at the time of the Reformation, and we can see other individuals in the history of the Church, both East and West. The tradition of the Fool-for-Christ, for example that of
St. Francis of Assisi in the Western Church, or
St. Basil the Blessed in the Eastern Church.
-CryptoLutheran