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"New" in this sense, is as in, "New covenant (or new testament, if you're going by a literal translation of the word covenant)." It is "new" as in it only 1200 (Aquinas wrote it), as opposed to the 4000(?) year old covenant of Abraham and the 2500 year old covenant of Moses.
It means that the believer is able to relate directly to the Godhead through the sacrifice of Christ, as opposed to the defective worship of the Old Testament (where the priest was mortal and sinful and had to offer sacrifice for his own sins in addition to the sins of the people and all of that other quasi-Pauline goodness from the book of Hebrews).
Upvote:3
Question: is "the New Rite" necessarily a proper noun, or could this be a general reference to all old forms of repetitive forms of worship being replaced by "true worship of the heart," which in turn grow stale and must be replaced by new energetic forms of worship?
This the translation I found at the Catholic Encyclopedia:
Down in adoration falling, Lo! the sacred Host we hail, Lo! oe'r ancient forms departing Newer rites of grace prevail; Faith for all defects supplying, Where the feeble senses fail.
The translation "newer rites" overtaking older ones would tend to support this position.