I believe that the gift of prophecy was essential in the first century (as is clear from the rest of the New Testament) for the communication of New Testament truth through the apostles in the early church because there was no completed canon of Scripture at that time. There are many today who believe the gift of prophecy still exists, but I do not believe this is correct. Now that we have the completed canon of Scripture, Old and New Testaments, the gift of prophecy is no longer needed. The author of Hebrews warned against ignoring the new revelation that has come to us through the New Testament message.
2:1 Therefore we must pay closer attention to what we have heard, so that we do not drift away. 2:2 For if the message spoken through angels proved to be so firm that every violation or disobedience received its just penalty, 2:3 how will we escape if we neglect such a great salvation? It was first communicated through the Lord and was confirmed to us by those who heard him, 2:4 while God confirmed their witness with signs and wonders and various miracles and gifts of the Holy Spirit distributed according to his will.
Note that he points out that this final aspect of revelation came first through the Son (the Lord Jesus), but that it was then confirmed to us (i.e., the first century Christians, not us today) by those who heard him (the apostles and Paul would be included here). This message was confirmed by sign and wonders distributed by the Spirit according to his will. But this miraculous confirmation was to the first century Christians. It was during this period that the gift of prophecy was active and the signs authenticated the prophets as God’s messengers (as given through the gift of prophecy) to those first century Christians who heard them. Our Lord spoke of this future process of revelation after His departure to the disciples in John 16:12f.
Since the early church did not have a completed canon, the gift of prophecy was also temporarily active in churches as in Corinth. Included here was the gift of discernment (cf. 1 Cor. 14 and 1 Thess. 5:19-21) to verify the accuracy of the message in others who had this gift. Of course, any prophetic message was also to be compared to the apostolic tradition that had been given to the church and if it did not conform or was contrary, it was to be rejected. Once God had finished giving the New Testament which took several years (the last book being written no later than about A.D. 90), the gift of prophecy ceased.
There is an excellent article called, Prophecy Rediscovered? A Review of the Gift of Prophecy in the New Testament and Today, by Robert L. Thomas from “Bibliotheca Sacra,” a theological journal from Dallas Seminary that I would highly recommend.