Perhaps the liturgical feast of the Chair of St Peter, celebrated on 22nd February, is most exactly a celebration of the office of the Successor Peter; but I nevertheless find the Solemnity of St Peter and St Paul on 29th June prompt to reflect on that office. I am left at a bit of a loss that clergy seem to shy away from preaching on the Papal office on this feast day.
Hans Urs von Balthasar makes great play of the way in which, though he arrives at the tomb first on Easter morning, St John waits for St Peter to catch up, and then allows that he should enter the tomb first. Though not in time - the first immediate witness is Mary Magdalene - this gives a certain precedence to St Peter's witness to the resurrection. It is reflected at the start of the liturgy of the Easter Sunday Mass in St Peter's Square, when the successor of St Peter venerates an image of the risen Christ in a testimony to the truth of the resurrection. Whilst both the charism of love (St John) and that of hierarchy (St Peter) are essential to the Church, the former charism gives precedence to the latter.
In the figures of St Paul and St Peter, a similar precedence can be seen. St Paul's mission to the Gentiles seeks its confirmation from the apostles gathered around St Peter in Jerusalem. Both represent essential features of the life of the Church; but St Paul shows a deference to St Peter that reflects that of St John.