Is Peter the leader of the Apostles?
Peter was certainly given instruction by Jesus to strengthen the disciples.
Luke 22: 31,32 And the Lord said, "Simon, Simon! Indeed, Satan has asked for you, that he may sift you (the disciples) as wheat. 32 "But I have prayed for you, that your faith should not fail; and when you have returned to Me, strengthen your brethren."
Paul tells us that Peter was the first apostle that Jesus appeared to after his resurrection.
1 Corinthians 15:4 and that He was buried, and that He rose again the third day according to the Scriptures, 5 and that He was seen by Cephas (Peter), then by the twelve.
After his resurrection Jesus again instructed Peter to be a shepherd to the flock:
John 21:15-17 So when they had eaten breakfast, Jesus said to Simon Peter, "Simon, son of Jonah, do you love Me more than these?" He said to Him, "Yes, Lord; You know that I love You." He said to him, "Feed My lambs." 16 He said to him again a second time, "Simon, son of Jonah, do you love Me?" He said to Him, "Yes, Lord; You know that I love You." He said to him, "Tend My sheep." 17 He said to him the third time, "Simon, son of Jonah, do you love Me?" Peter was grieved because He said to him the third time, "Do you love Me?" And he said to Him, "Lord, You know all things; You know that I love You." Jesus said to him, "Feed My sheep."
Peter took the lead in organizing a replacement for Judas Iscariot.
Acts 1:15-26 And in those days Peter stood up in the midst of the disciples (altogether the number of names was about a hundred and twenty), and said, 16 "Men and brethren, this Scripture had to be fulfilled, which the Holy Spirit spoke before by the mouth of David concerning Judas, who became a guide to those who arrested Jesus; 17 "for he was numbered with us and obtained a part in this ministry." 18 (Now this man purchased a field with the wages of iniquity; and falling headlong, he burst open in the middle and all his entrails gushed out. 19 And it became known to all those dwelling in Jerusalem; so that field is called in their own language, Akel Dama, that is, Field of Blood.) 20 "For it is written in the book of Psalms: ‘Let his dwelling place be desolate, And let no one live in it’; and, ‘Let another take his office.’ 21 "Therefore, of these men who have accompanied us all the time that the Lord Jesus went in and out among us, 22 "beginning from the baptism of John to that day when He was taken up from us, one of these must become a witness with us of His resurrection." 23 And they proposed two: Joseph called Barsabas, who was surnamed Justus, and Matthias. 24 And they prayed and said, "You, O Lord, who know the hearts of all, show which of these two You have chosen 25 "to take part in this ministry and apostleship from which Judas by transgression fell, that he might go to his own place." 26 And they cast their lots, and the lot fell on Matthias. And he was numbered with the eleven apostles.
Peter acted as the spokesman at Pentecost:
Acts 2:14-36 But Peter, standing up with the eleven, raised his voice and said to them, "Men of Judea and all who dwell in Jerusalem, let this be known to you, and heed my words. 15 "For these are not drunk, as you suppose, since it is only the third hour of the day. 16 "But this is what was spoken by the prophet Joel: 17 ‘And it shall come to pass in the last days, says God, That I will pour out of My Spirit on all flesh; Your sons and your daughters shall prophesy, Your young men shall see visions, Your old men shall dream dreams. 18 And on My menservants and on My maidservants I will pour out My Spirit in those days; And they shall prophesy. 19 I will show wonders in heaven above And signs in the earth beneath: Blood and fire and vapor of smoke. 20 The sun shall be turned into darkness, And the moon into blood, Before the coming of the great and awesome day of the LORD. 21 And it shall come to pass That whoever calls on the name of the LORD Shall be saved.’ 22 "Men of Israel, hear these words: Jesus of Nazareth, a Man attested by God to you by miracles, wonders, and signs which God did through Him in your midst, as you yourselves also know— 23 "Him, being delivered by the determined purpose and foreknowledge of God, you have taken by lawless hands, have crucified, and put to death; 24 "whom God raised up, having loosed the pains of death, because it was not possible that He should be held by it. 25 "For David says concerning Him: ‘I foresaw the LORD always before my face, For He is at my right hand, that I may not be shaken. 26 Therefore my heart rejoiced, and my tongue was glad; Moreover my flesh also will rest in hope. 27 For You will not leave my soul in Hades, Nor will You allow Your Holy One to see corruption. 28 You have made known to me the ways of life; You will make me full of joy in Your presence.’ 29 "Men and brethren, let me speak freely to you of the patriarch David, that he is both dead and buried, and his tomb is with us to this day. 30 "Therefore, being a prophet, and knowing that God had sworn with an oath to him that of the fruit of his body, according to the flesh, He would raise up the Christ to sit on his throne, 31 "he, foreseeing this, spoke concerning the resurrection of the Christ, that His soul was not left in Hades, nor did His flesh see corruption. 32 "This Jesus God has raised up, of which we are all witnesses. 33 "Therefore being exalted to the right hand of God, and having received from the Father the promise of the Holy Spirit, He poured out this which you now see and hear. 34 "For David did not ascend into the heavens, but he says himself: ‘The LORD said to my Lord, "Sit at My right hand, 35 Till I make Your enemies Your footstool."’ 36 "Therefore let all the house of Israel know assuredly that God has made this Jesus, whom you crucified, both Lord and Christ." that dwell at Jerusalem, be this known unto you, and hearken to my words:
Peter dealt with Ananias and Sapphira.
Acts 5:1 But a certain man named Ananias, with Sapphira his wife, sold a possession. 2 And he kept back part of the proceeds, his wife also being aware of it, and brought a certain part and laid it at the apostles’ feet. 3 But Peter said, "Ananias, why has Satan filled your heart to lie to the Holy Spirit and keep back part of the price of the land for yourself? 4 "While it remained, was it not your own? And after it was sold, was it not in your own control? Why have you conceived this thing in your heart? You have not lied to men but to God." 5 Then Ananias, hearing these words, fell down and breathed his last. So great fear came upon all those who heard these things. 6 And the young men arose and wrapped him up, carried him out, and buried him. 7 Now it was about three hours later when his wife came in, not knowing what had happened. 8 And Peter answered her, "Tell me whether you sold the land for so much?" She said, "Yes, for so much." 9 Then Peter said to her, "How is it that you have agreed together to test the Spirit of the Lord? Look, the feet of those who have buried your husband are at the door, and they will carry you out." 10 Then immediately she fell down at his feet and breathed her last. And the young men came in and found her dead, and carrying her out, buried her by her husband. 11 So great fear came upon all the church and upon all who heard these things.
Peter caused Dorcas to be restored to life.
Acts 9:40 But Peter put them all out, and knelt down and prayed. And turning to the body he said, "Tabitha, arise." And she opened her eyes, and when she saw Peter she sat up.
Peter was the one Cornelius was told to send for.
Acts 10:5 Now send men to Joppa, and send for Simon whose surname is Peter.
He became the first one to preach to the gentiles, though primarily he preached only to Jews.
Acts 15:7 And when there had been much dispute, Peter rose up and said to them: "Men and brethren, you know that a good while ago God chose among us, that by my mouth the Gentiles should hear the word of the gospel and believe.
Peter was the one who Paul went to see after his conversion.
Galatians 1:18 Then after three years I went up to Jerusalem to see Peter, and remained with him fifteen days.
After Acts 15 the emphasis shifts to Paul.
Peter wasn’t perfect.Paul writes:
Galatians 2:11 Now when Peter had come to Antioch, I withstood him to his face, because he was to be blamed
I hope this helps.