The Liturgical Arts Journal website has an interesting article for the Feast of Christ the King by the Oxford based music historian Thomas Neal. In it, the second of three articles, he writes about the music appropriate to the Feast of Christ the King - be it EF or OF - and discusses how the ancient text, and chants, of the Laudes Regiae can be, and have been, adopted for the modern feast instituted in 1925. The distinctive refrain of Christus vincit! Christus regnat! Christus imperat! used in medieval Royal liturgical acclamations, and as an inscription on some French royal coin issues in the eighteenth century, has found a new performance space to celebrate the Kingship of Christ.
The article can be seen at Christus Vincit! Music for the feast of Christ the King (Part 2 of 2) This has a useful bibliography for those who wish to explore the subject further