"The stewards are chosen by the king or by a prophet."

What makes someone a prophet?  In the Old Testament, there is a moment of prophetic call in which God gives His spirit to the prophet.  Moses encounters God in the burning bush, Isaiah's lips are cleansed by the burning coal, and Elijah even leaves his prophetic spirit on his successor, Elisha.

After the Resurrection, Jesus gives the Holy Spirit to the Apostles.  As we see in John 20, He breathes on them and says "Receive the Holy Spirit."  Later, in Acts, the Apostles appoint others to carry out the work of the Church in their absence by the laying on of hands, which imparts the Holy Spirit.  Likewise, in his letters, Paul speaks often of members of the faithful prophecying or speaking in tongues, and of how it ought to be used for the building up of the church.

Certainly, then, the Apostles are prophets in the New Covenant, for they have the Holy Spirit.  We see them exercising their prophetic authority to see to the governance of the Church.  In the first chapter of Acts, Peter calls upon the Apostles to exercise this authority to name a new Apostle to fill the place of Judas, and thus Matthias is brought into their ranks.

This is remarkable, for previously, only Jesus claimed to possess the authority to appoint the Twelve.  However, after the Ascension, it is clear that the Apostles understand this authority to have been passed on to them.  Why, then, should the college of the Apostles and their successors not have the authority to appoint a successor to Peter?