The phrase Apostolic Age is derived from ἀπόστολος, G693, (Ezra 7:14; Dan 5:24). Meaning: that period of Early Church history during the life and work of the original apostles, which extended from the day of Pentecost (c. A.D. 33; Acts 2, to the death of John, c. A.D. 100). The main sources for the period are the Book of Acts and the NT letters.
The period from Pentecost to the death of John, the last of the twelve apostles (ca 100), when the Church was under the guidance of Paul (till his death) and the apostles, especially Peter and John.
When the disciples realized that they had seen the risen Christ for the last time and that it had now become their duty to spread His message, they gathered themselves together and restored the number of "witnesses" to the appointed Twelve. Immediately afterward the outpouring of the Holy Spirit gave them the signal to begin work.