Paul was the 12th apostle, replacing Judas. As usual for Peter, he jumped the gun and didn't wait for the Holy Spirit, but used a gambling technique to fill the place of Judas with one of the 70.
1stCenturyLady, when you speak of the casting of lots in Acts 1 and Matthias being chosen in the place of Judas there by a gambling technique (I'll just post it below)
Acts.1
[13] And when they were come in, they went up into an upper room, where abode both Peter, and James, and John, and Andrew, Philip, and Thomas, Bartholomew, and Matthew, James the son of Alphaeus, and Simon Zelotes, and Judas the brother of James.
[14] These all continued with one accord in prayer and supplication, with the women, and Mary the mother of Jesus, and with his brethren.
[15] 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,)
[16] 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.
[17] For he was numbered with us, and had obtained part of this ministry.
[18] Now this man purchased a field with the reward of iniquity; and falling headlong, he burst asunder in the midst, and all his bowels gushed out.
[19] And it was known unto all the dwellers at Jerusalem; insomuch as that field is called in their proper tongue, Aceldama, that is to say, The field of blood.
[20] 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.
[21] Wherefore of these men which have companied with us all the time that the Lord Jesus went in and out among us,
[22] 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.
[23] And they appointed two, Joseph called Barsabas, who was surnamed Justus, and Matthias.
[24] And they prayed, and said, Thou, Lord, which knowest the hearts of all men, shew whether of these two thou hast chosen,
[25] That he may take part of this ministry and apostleship, from which Judas by transgression fell, that he might go to his own place.
[26] And they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles.
The casting of lots is what they did as far back as Moses as is shown back further and going forward (after Moses died) as shown us in Joshua in respects to their inheritance
The LORD having commanded lots
Josh 14:2 By lot was their inheritance, as the LORD commanded by the hand of Moses, for the nine tribes, and for the half tribe.
And so similarly under Peter's oversight it says
Acts 1
[26] And they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles.
Would you think it at all possible that it could have been after the death of James by Herod (In Acts 12:2) rather than Judas death by his own hand that Paul's apostleship moves into place?
Because here it shows us
Acts 12
[1] Now about that time Herod the king stretched forth his hands to vex certain of the church.
[2]And he killed James the brother of John with the sword.
And the very next chapter is where the Holy Ghost is now setting apart Saul/Paul and Barnabas for the work he called them to here
Acts.13
[1] Now there were in the church that was at Antioch certain prophets and teachers; as Barnabas, and Simeon that was called Niger, and Lucius of Cyrene, and Manaen, which had been brought up with Herod the tetrarch, and Saul.
[2] As they ministered to the Lord, and fasted, the Holy Ghost said, Separate me Barnabas and Saul for the work whereunto I have called them.
[3] And when they had fasted and prayed, and laid their hands on them, they sent them away.
[4] So they, being sent forth by the Holy Ghost, departed unto Seleucia; and from thence they sailed to Cyprus.
And the next chapter (at Lystra) is where we find Paul and Barnabas referred to as apostles for the first time in Acts.
Acts.14
[14] Which when the apostles, Barnabas and Paul, heard of, they rent their clothes, and ran in among the people, crying out....
See what I mean?