Psalm 33:3 says “Sing to the LORD a new song.” This cannot amount to a claim that some completely new stage in redemption has occurred every day or every time this verse is read. It must mean “sing a fresh song – a song that may sometimes be old words with fresh life and will sometimes be a song with new words; but most importantly a song that is fresh because it comes from a fresh, and possibly completely new, realisation and appreciation of how wonderful the LORD and his mighty deeds are.”
God is infinitely great, loving and delightful; and his works are wonderful, both his work of creation and even more so his gracious work of redemption in his eternal Son. We can never take all this in; and even when we do take in some of it, through his word and the inner work of his Spirit, it’s like an encounter with another person: your mind may change, you may come permanently to have new thoughts and views, but you also want to meet that person again (if they are good), you want a fresh encounter. In urging us to sing a new song to the LORD, Psalm 33 is bidding us seek fresh encounters with the living God daily, some of which will also give us fresh insights; but even those that don’t change or expand our view of reality will be meetings with him that enable us to sing his praise with fresh reality and joy.
Such experiences of God are possible because God’s compassion is so vast and is new every morning; these experiences should be sought, and can then result in the outward expression of singing – let it be so!
Now we are God's children 
Very encouraging – do you think this passage also supports the regular writing of new songs to sing as well as the continuous praise element you refer to?
Don’t see why not. Both and.
Chris – stimulating article.
I am regularly encouraged by people posting old hymns on Facebook with a fresh impact on what it means to them in a present situation.
In addition to what you have said do you think this also supports regularly writing new songs as well as recalling old ones with fresh delight?
How does this fit with those who would subscribe to the regulative principle? What would be their explanation of this verse?
The exclusive Psalmody regulative principle folk? I don’t know what they do with this verse, though in a way it is easy to imagine what they might: adopt my interpretation of it and it doesn’t imply new words at all, necessarily!