Most Christians react very negatively to any suggestion that apostles (Heb. sh'liachim) could or should exist today. It is true that Jesus (Yeshua) personally chose and called the 12, and spent His entire ministry living with them, eating with them, and teaching them, 24 hours a day, 7 days a week. This, of course, uniquely qualified them for their callings. I would never suggest that anyone today could meet these same qualifications, nor deny that this is a significantly special preparation.
However, when we examine Sacred Scripture closely, we find that the aversion to others being apostles is not really biblically founded, but emotionally rooted.
The Apostle Paul wrote that the resurrected Savior appeared to “the Twelve” and later to “all the apostles” (1 Corinthians 15:3-8). The clear implication here is that there were other apostles outside the special 12. We also find several others outside the 12 referred to as Apostles in 1 Thessalonians 1:1 and 2:6. Romans 16:7 seems to imply that Andronious and Junias were considered Apostles as well. In Acts 14:14, Luke referred to Barnabas as an Apostle. Then in Galatians 1:18-19 and 2:9 we find James, the brother of Jesus, numbered among the Apostles. Apparently the 1st century community of disciples did not share the modern aversion to the idea of Apostles other than the 12. Is there a difference between these two "classes" of Apostles?
The 12 are unique not only in their having lived and studied directly at the feet of Yeshua, but also in their having been witnesses to the resurrected Messiah. This would have qualified James and Paul to be Apostles, since both were witnesses to His resurrection as well. These men were called by Jesus to be His representatives in a very unique way. (1 Corinthians 15:8-9; Galatians 1:11-2:10) These men were sent out by Yeshua in person, while the other "class" of Apostle is called and sent out by Yeshua in Spirit. They are witnesses to the truth of the resurrection and successors of the 12 in their ministry to lead, teach and evangelize. (Acts 13:1-3; 2 Corinthians 8:23) They are responsible to faithfully transmit and keep that which the original 12 Apostles taught, and to preserve the "faith once delivered to the saints."(Jude 1:3)
Based on Acts 1-7, 8:12, 15:1-2 and 21:17-18, it seems likely that most of the 12 Apostles were centered in Jerusalem for a number of years. While there, the 12 were mostly engaged in sharing the Good News with their fellow Jews and organizing the local community of disciples. That did not remain the case, since when Paul made his journey to Jerusalem, all indications are that the 12 had left to other lands to spread the faith, and only James was left. (Acts 21:17-18). History and the writings of the Ante-Nicene Fathers tell us that the 12 became traveling teachers, spreading the Good News, founding congregations, and then moving on to the next place, sometimes returning to previous places to continue teaching. Paul followed this same pattern. He spent a little over a year in Corinth (Acts 18:11), roughly 2 years in Ephesus (Acts 19:8-10), and 2 years in Rome (Acts 28:31).
The second "class" of Apostles should follow this same tradition in a contemporary context. Modern Apostles do not bring any new teachings, no new practices, nor any new prophecies. They merely teach and lead the congregations, appoint elders to tend the local congregation in their absence, and defend the Apostolic traditions they have received. If Apostles are extinct, it is only because Christians have misunderstood them and their role for a very long time.