Like the following sister psalm 112, this is a hymn of thanks and praise for gracious divine love, guidance and protection. An acrostic poem in the Hebrew, it may have been used for instruction.
All the powerful key words of the psalter seem purposefully gathered in a pile. Besides those already mentioned from early verses, we are assured that:
7 The works of God's hands are faithful and just; all the precepts are sure. 8 Standing fast for ever and ever, wrought in truth and equity.
Few can deny that truth and equity have been in short supply over the years. There’s no sign of the need abating, so the implication is that more régimes could pay attention.

Sure enough at the end of the song, the psalmist drops in a response, encouraging the reader — hopefully including rulers and governments — to ‘fear God’. No quaking, subservient reaction is intended, but one of appreciative recognition and adherence to the principles of all those key words, if not to the Christian God per se. A more positive explanation may be to honour the best of divine sponsorship and influence.
According to many psalms, the benefits of such allegiance is safety, guidance, confidence, ways of truth, victory over evil, and peace. Here, rather surprisingly but also thought-provoking and exciting, the follower is promised wisdom:
10 The fear of God is the beginning of wisdom; all those who practise it have a good understanding. God's praise endures for ever.
Well, if this whets your appetite for more discussion on wisdom plus also some of the music of this psalm — and oh by the way name-dropping Erasmus and the Humanist Library — please read on from here in the main page ‘Psalm 111: Learn wisdom, truth, equity’>
🎵
Yes, there is plenty of music, both classical and modern. In the former category, just search for Confitebor tibi Domine ( ‘I will give thanks unto the Lord’, verse 1, BCP.). Works by Mozart, Victoria (his vespers psalm included) and Schütz appear in a long list. This search does not guarantee that the text is from Psalm 111 (110 Vulgate), but most are.

Monteverdi, for example, wrote five pieces using this text. His Confitebor I for soprano with string ensemble of two violins and basso continuo, was first published in 1650 in Messa a quattro voci et salmi concertati, no. 4. Here is Julie Roset singing the motet by Monteverdi at the Namur festival in Belgium, 2018:
For those using Together in Song, see no 68, a refrain by Jane Marshall with a double tone; or Psalms for All Seasons 111C.
Here is another easy solution, tune source unknown, arranged by the author:

- At South Woden: we enjoy a combined service at St James, Curtin. Your cantor will sing the psalm using the refrain shown above. Verses will be freely adapted to the same tune, rather than the tone in the first four bars.