The Gospels fulfill the Prophets
10 Concerning this salvation, the prophets, who spoke of the grace that was to come to you, searched intently and with the greatest care,
11 trying to find out the time and circumstances to which the Spirit of Christ in them was pointing when he predicted the sufferings of Christ and the glories that would follow.
12 It was revealed to them that they were not serving themselves but you, when they spoke of the things that have now been told you by those who have preached the gospel to you by the Holy Spirit sent from heaven. Even angels long to look into these things.
The Greek here is not easy to translate, and the NIV does a good job, so I have used it.
Peter is reminding his readers and listeners of the salvation history which lies behind our salvation; Christ did not just appear from nowhere. The prophets were guided to the knowledge of the Messiah and predicted His coming. They were guided by ‘the Spirit of Christ’, or the Holy Spirit, so we know that what we call the OT was also an inspired text. But, as with Our Lady, they were not mere puppets, they pondered, they wrestled, they engaged with the Spirit; so must we.
Christ Himself referred to the prophets in Luke 24:25-27, and it is natural that Peter should have recalled those words which he echoes here. Although he does not name the prophet, the commentators are agreed that it was Isaiah .
Again, we see a theme touched on earlier, the connection between suffering and glory; in 5:1 he will explicitly identify himself as ‘a witness to the sufferings of Christ and one who has a share in the glory to be revealed.’
Peter himself is passing on that teaching and its insights; he is the latest prophet in this sense. We see, yet again, the importance of tradition. That what has been revealed and given to us is something for which the angels longed is further confirmation, were it needed, of the extraordinary gift He has given us.