The words “et reliqua” means “and the rest” or “and so on”
What I’m referring to below is the Breviarium Monasticum or Monastic Breviary on Sundays (three nocturns).
During the office, just this part of the gospel is read, including “Et reliqua”. This is followed by the remaining 3 lessons, most likely the homily, in the third nocturn and then the Te Deum. Once the Te Deum is completed, then this assigned gospel for the day is read in its entirety again. This is also spelled out in Chapter 11 of the Rule of St Benedict.
Now, as far as the Roman Office is concerned, I think they only read the first part of the gospel with “et reliqua” and then that’s it. They don’t go back and read it in its entirety. BUT, I could be wrong, although that’s what I seem to remember.
So, basically, if you’re praying the Roman office, that’s all that is said. In the Monastic Office, you would read the entire gospel after Te Deum. You can select the Pre-Trident Monastic option to see how the Monastic compares to the Roman on Divinum Officium. The Monastic option can be hit or miss sometimes.
Keep in mind, though, the site
divineoffice.org refers to the current Liturgy of the Hours which will be quite different than the Roman or Monastic offices.
Hope this helps!
Robert