“after the resurrection of our Savior from the dead and His assumption into heaven, the Apostles, who had been sent forth by Him, as He Himself had been sent forth by the Father, into all the world, and had received all authority to bind and loose and all the gracious gifts of the All-holy Spirit on the day of Pentecost, they not only possessed the name of Apostle by virtue of the facts of themselves, but indeed even the name of Bishop (overseer) as sacred Epiphanius bears witness (Her. 27): ‘First were Peter and Paul, these two Apostles and Bishops’” (Pedalion 2)
Accepting the above, during the meal at the shore - the other Apostles were present, and yet Our Lord said only unto Peter :-
St John 21
 Simon Peter went up, and drew the net to land, full of great fishes
, one hundred and fifty-three. And although there were so many, the net was not broken.  Jesus saith to them: Come, and dine. And none of them who were at meat, durst ask him: Who art thou? knowing that it was the Lord.  And Jesus cometh and taketh bread, and giveth them, and fish in like manner.  This is now the third time that Jesus was manifested to his disciples, after he was risen from the dead.  When therefore they had dined, Jesus saith to Simon Peter: Simon son of John,
lovest thou me more than these? He saith to him: Yea, Lord, thou knowest that I love thee. He saith to him: Feed my lambs
 He saith to him again: Simon, son of John,
lovest thou me? He saith to him: Yea, Lord, thou knowest that I love thee. He saith to him: Feed my lambs
.  He said to him the third time: Simon, son of John, lovest thou me?
Peter was grieved, because he had said to him the third time: Lovest thou me? And he said to him: Lord, thou knowest all things: thou knowest that I love thee. He said to him: Feed my sheep.
 Amen, amen I say to thee, when thou wast younger, thou didst gird thyself, and didst walk where thou wouldst. But when thou shalt be old, thou shalt stretch forth thy hands, and another shall gird thee, and lead thee whither thou wouldst not.  And this he said, signifying by what death he should glorify God. And when he had said this, he saith to him: Follow me.  Peter turning about, saw that disciple whom Jesus loved following, who also leaned on his breast at supper, and said: Lord, who is he that shall betray thee?
 Him therefore when Peter had seen, he saith to Jesus: Lord, and what shall this man do?  Jesus saith to him: So I will have him to remain till I come, what is it to thee? follow thou me.  This saying therefore went abroad among the brethren, that that disciple should not die. And Jesus did not say to him: He should not die; but, So I will have him to remain till I come, what is it to thee?  This is that disciple who giveth testimony of these things, and hath written these things; and we know that his testimony is true.  But there are also many other things which Jesus did; which, if they were written every one, the world itself, I think, would not be able to contain the books that should be written. "Feed my sheep"... Our Lord had promised the spiritual supremacy to St. Peter; St. Matt. 16. 19; and here he fulfils that promise, by charging him with the superintendency of all his sheep, without exception; and consequently of his whole flock, that is, of his own church.