Are Priests successors of Apostles?
Absolutely. The Catholic faith is the only faith that can trace itself back to the time of the Apostles. Whereas the Greek word for priest is not used for the Apostles, we have priestly functions attached to their ministry work constantly. Furthermore, the Greek term for elder/presbyter, has priestly functions tied in with it throughout many passages in the New Testament. A particular passage of interest for us is Acts 1:20-26
We will examine the NASB rendering.
20"For it is written in the book of Psalms,
'(D)LET HIS HOMESTEAD BE MADE DESOLATE,
AND LET NO ONE DWELL IN IT';
'(E)LET ANOTHER MAN TAKE HIS OFFICE.'
21"Therefore it is necessary that of the men who have accompanied us all the time that (F)the Lord Jesus went in and out among us--
22(G)beginning with the baptism of John until the day that He (H)was taken up from us--one of these must become a (I)witness with us of His resurrection."
23So they put forward two men, Joseph called Barsabbas (who was also called Justus), and (J)Matthias.
24And they (K)prayed and said, "You, Lord, (L)who know the hearts of all men, show which one of these two You have chosen
25to occupy (M)this ministry and (N)apostleship from which Judas turned aside to go to his own place."
26And they (O)drew lots for them, and the lot fell to (P)Matthias; and he was added to (Q)the eleven apostles.
The Biblical Greek word for OFFICE is very important to our examination.
We find the word Episkopeyn from EPISKOPEE.
What Luke is focusing on, is the fact that the office will be occupied by another, continuing the succession. In this case, the prayer to GOD helps guide them in choose Matthias to fill the vacancy that Judas had left.
The prayer begins with the all important su. ku,rie
The band of Apostles knew that GOD had promised to not leave them. GOD had promised to remain with them forever. Therefore it was not inconceivable to call upon the LORD for this guidance in choosing a successor.