According to Acts 1:15-26, during the days after the Ascension, Peter stood up in the midst of the brothers (about 120 of Jesus followers). Now that Judas had betrayed his ministry, it was necessary, Peter said, to fulfill the scriptural recommendation: May another take his office. Therefore, it is necessary that one of the men who accompanied us the whole time the Lord Jesus came and went among us, beginning from the baptism of John until the day on which he was taken up from us, become with us a witness to his resurrection (Acts 1:21-22).
They nominated two men: Joseph Barsabbas and Matthias. They prayed and drew lots. The choice fell upon Matthias, who was added to the Eleven.
Matthias is not mentioned by name anywhere else in the New Testament.