Sacrosanctum Concilium devotes Chapter IV, the next nineteen sections to “The Divine Office,” or the Liturgy of the Hours.
Let me preface these next 19 posts by saying the reform of the Office is conceded as one of the big disappointment of the Council, at least in progressive circles. I would concur.
Christ Jesus, high priest of the new and eternal covenant, taking human nature, introduced into this earthly exile that hymn which is sung throughout all ages in the halls of heaven. He joins the entire community of (hu)mankind to Himself, associating it with His own singing of this canticle of divine praise.
Christ is the source of the introduction of heaven’s liturgy among believers on Earth. The Liturgy of the Hours is not so much part of the domain of clergy and religious, but the prayer of Christ and of the sainted and angelic believers in heaven.
For he continues His priestly work through the agency of His Church, which is ceaselessly engaged in praising the Lord and interceding for the salvation of the whole world. She does this, not only by celebrating the eucharist, but also in other ways, especially by praying the divine office.
Christ acts as a priest through the celebration of earthly liturgy: the Eucharist, certainly. But also the Hours.