=I can't find anything in Scripture saying that Peter or any other apostle state that their apostolic authority would be passed on to successors either. Would someone please direct me to the biblical references on this issue? Thank you.
Acts 1
20"For," said Peter, "it is written in the book of Psalms,
" 'May his place be deserted;
let there be no one to dwell in it,' and,
" 'May another take his place of leadership.'
21Therefore it is necessary to choose one of the men who have been with us the whole time the Lord Jesus went in and out among us,
22beginning from John's baptism to the time when Jesus was taken up from us. For one of these must become a witness with us of his resurrection."
23So they proposed two men: Joseph called Barsabbas (also known as Justus) and Matthias.
24Then they prayed, "Lord, you know everyone's heart. Show us which of these two you have chosen
25to take over this apostolic ministry, which Judas left to go where he belongs."
26Then they cast lots, and the lot fell to Matthias; so he was added to the eleven apostles.
2 Tim 2:2
2And the things you have heard me say in the presence of many witnesses entrust to reliable men who will also be qualified to teach others.
Also, from St. Clement, who was ordained by Peter:
"And thus preaching through countries and cities, they appointed the first-fruits [of their labours], having first proved them by the Spirit, to be bishops and deacons of those who should afterwards believe. Nor was this any new thing, since indeed many ages before it was written concerning bishops and deacons. For thus saith the Scripture a certain place, 'I will appoint their bishops s in righteousness, and their deacons in faith.'... Our apostles also knew, through our Lord Jesus Christ, and there would be strife on account of the office of the episcopate. For this reason, therefore, inasmuch as they had obtained a perfect fore-knowledge of this, they appointed those [ministers] already mentioned, and afterwards gave instructions, that when these should fall asleep, other approved men should succeed them in their ministry...For our sin will not be small, if we eject from the episcopate those who have blamelessly and holily fulfilled its duties."
Pope Clement, Epistle to Corinthians, 42, 44 (A.D. 98).