Do the offices of apostle and prophet still exist in the church today?
The title "apostle" means one sent with a message, and it is a special office in the history of the church. Apostles were men who were appointed by Christ through a personal appearing (e.g. Paul on the road to Damascus) to hold the office. Only those who have personally witnessed the risen Christ in the flesh and received a commission directly from Him may assume this title. There were more than twelve apostles appointed in the early church, and these men lived until the end of the first century, which is why Paul still refers to this office as active in Ephesians 4:11. When the last apostle, John, died at the end of the first century, the office of apostle ceased to exist in the church.
Christ established this office to author the New Testament canon through these men, and they were given unique miraculous powers to validate their ministry and authenticate their teaching. For example, the apostle Paul told the church in Corinth they could trust his word over that of false teachers because his powers validated his ministry:
Paul told Corinth that those who claimed to have authority by their words must demonstrate they also possess the power that came with apostolic authority otherwise they were not legitimate authority figures in the church. Such a test no longer exists in the church because the apostolic office no longer exists. In place of apostles we have the full counsel of God's word.
Unfortunately, men (and even women) uninformed by the word of God or deceived by false teaching may attempt to appropriate this title for themselves, just as false apostles existed in the early church. In all cases, false apostles are shown to be counterfeits because they cannot perform the miracles required to validate their title. All apostles were given unique gifts of the spirit to validate their positions of authority. Christ told the apostles they could cast out demons, heal the sick, raise the dead and receive fatal snake bites but not die. Though the Lord may permit an individual Christian to do one or more of these miracles in rare cases, they are not normal Christian gifts; they were unique to apostles.
You can learn more about why the Lord established the office of apostle in the early church (and why it no longer exists) in our Acts of the Apostles Bible study.
The office of prophet is also misunderstood. The Bible uses the term prophet to describe a man gifted to deliver God's revelation to men. A prophet's words were recorded and eventually made a part of the canon of scripture. The office of prophet carries significant responsibilities and burdens, according to scripture. Specifically, the Bible says this concerning the office of prophet:
The Bible taught Israel that anyone claiming the office of prophet was required to be 100% correct in ALL prophecies. If a supposed prophet was ever incorrect in their prophetic utterances - even just once - then they were to be put to death, according to the word. Many churches fail to understand this rigorous standard for prophecy required by scripture, and therefore we are tempted to assign this title too easily to those who wish to claim it. In reality, the biblical office of prophet no longer exists in the church, since the canon of scripture has been completed.
Nevertheless, the Lord may bring supernatural insight concerning future events to anyone at anytime, but such a moment doesn't mean the person has become a prophet in the biblical sense. It simply means God has chosen to reveal something to them at a point in time for a certain purpose. This type of prophecy shouldn't be mistaken for the office of prophet.
Many men and women go around in the church proclaiming themselves to be prophets, but if we apply the test God gives us in Deuteronomy, we quickly find these people to be frauds deceiving believers. Remember this exchange in Jeremiah:
In the church today, we find no evidence of apostles nor prophets operating as the Bible requires. Instead, we may find an occasional person given insight of future events on an occasional basis, but mostly we find frauds claiming to have powers they cannot validate in the way the Bible requires.