Need to replace Judas:
Acts 1:12-16 And in those days Peter stood up in the midst of the disciples, and said, (the number of names together were about an hundred and twenty,) Men and brethren, this scripture must needs have been fulfilled, which the Holy Ghost by the mouth of David spake before concerning Judas, which was guide to them that took Jesus.
Requirements:
Acts 1:20-22 For it is written in the book of Psalms, Let his habitation be desolate, and let no man dwell therein: and his bishoprick let another take. Wherefore of these men which have companied with us all the time that the Lord Jesus went in and out among us, Beginning from the baptism of John, unto that same day that he was taken up from us, must one be ordained to be a witness with us of his resurrection.
(This rules out Paul as the 12th Apostle)
The 12th Apostle
Acts 1:23-26 And they appointed two, Joseph called Barsabas, who was surnamed Justus, and Matthias. And they prayed, and said, Thou, Lord, which knowest the hearts of all men, shew whether of these two thou hast chosen, That he may take part of this ministry and apostleship, from which Judas by transgression fell, that he might go to his own place. And they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles.
Matthias means “gift of Yahweh”. Matthias became one of the Twelve, replacing Judas after that disciple’s betrayal of Jesus. There is no further information about him in the New Testament. It is believed that Matthias placed his faith in Jesus Christ above everything else and was present with the other apostles at the Pentecost.