And again, the answer is found in Scripture. And the answer is NO.
The apostles had no successors, for to succeed them one needed to be a witness of Christ's resurreciton...
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." -- Acts 1:21-22"Wherefore of these men which have companied with us all the time that the Lord Jesus went in and out among us,
St. James the Greater is killed in Acts 12.
Was St. James of Jerusalem in Acts 15 an apostle or an elder?
Even if the requirements of Acts 1 were those of the Holy Spirit, and not just the prudential judgment of the 11 remaining apostles (remember the Holy Spirit had not yet fully descended then), those requirements were clearly waived when the other apostles accepted St. Paul among their number.