At the Saint Jean de Malte Community in France it is used throughout the year as the responsorial psalm at Mass, at Glenstal Abbey a section is sung by a solo voice as the response to the Scripture reading at the Office of Readings.
For those using Common Worship: Daily Prayer Psalm 119 could provide the psalmody for a Mid-Day Prayer, or a section be used daily as a response to Scripture at Morning or Evening Prayers. For those using The Divine Office three sections could be used each day one each after the two readings at the Office of Readings and one as the psalm at Mass. Praying sections of the psalm would also work well as part of the prayers of preparation for Mass.
This booklet, using the Grail version, provides a simple form of Daytime Prayer for use throughout the year and using the psalm over a week with simple refrains.:
And here is the modernised version of Knox’s acrostic version: