Yes, the five-fold ministry of Ephesians 4 — including that of apostles — is still in effect today. However, it is important that we clearly define the meaning of the word “apostle.”
The Greek word literally means a delegate, or one who is sent as an ambassador. The original 12 apostles were chosen by Christ for the specialized purpose of founding and organizing the church. The qualifications to be one of this special group of apostles is given in Acts 1. After the betrayal of Jesus by Judas, Matthias was picked to join the twelve based on one main requirement: that an apostle be a witness of the ministry and resurrection of Christ.
Paul, the apostle born out of season, met this qualification as a witness of Jesus’ resurrection on the road to Damascus. He was consequently commissioned by God to be the apostle to the Gentiles (Romans 11:13). Paul’s apostolic authority seems to have been commensurate with the original 12 apostles. Indeed, some scholars hypothesize that he was God’s choice to replace Judas rather than Matthias.
The Scripture does refer to other apostles (or delegates) such as Andronicus and Junia (Romans 16:7). These men, as well as others, were called of God with a mission to represent Him. While their authority may not have been on the same level as the original twelve, they did qualify Scripturally to be referred to as apostles.
Today’s apostles do not replace the original 12. However, God still has chosen delegates, “for the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ (Ephesians 4:12).”