Among the priests of the temple, the high-most position was not one of life-long duration, but rotated by turn among the many priests.
Caiaphas, being the chief priest at the time of the crucifixion of Jesus, prophesied concerning the situation as can be seen written of in John 11 [from Young's Literal Translation]
45 Many, therefore, of the Jews who came unto Mary, and beheld what Jesus did, believed in him;A moment's interruption here, for this Mary was sister to Martha, and to Lazarus, whom the one known to us today as Jesus Christ raised [Lazarus] from the grave, as is detailed in in the same chapter link has been given to.
46 but certain of them went away unto the Pharisees, and told them what Jesus did;47 the chief priests, therefore, and the Pharisees, gathered together a sanhedrim, and said, `What may we do? because this man doth many signs?
48 if we may let him alone thus, all will believe in him; and the Romans will come, and will take away both our place and nation.'
49 and a certain one of them, Caiaphas, being chief priest of that year, said to them, `Ye have not known anything,
50 nor reason that it is good for us that one man may die for the people, and not the whole nation perish.'
51 And this he said not of himself, but being chief priest of that year, he did prophesy that Jesus was about to die for the nation,
There is no suggestion I am aware of that the Papacy was meant to be a continuation of the Moses seat; and I can say with certainty that there is no evidence that the Bishop of Rome, or any other diocese, was ever a rotating position.