Not really - Christ through Paul points to the Psalms - the Psalms point to new songs - we are his chosen people, a royal priesthood - we are to sing new songs to His praise as the Psalms direct.
I have already asked for exegetical work to substantiate such an assertion yet none has been forthcoming.
Contextually (Ps. 96) it is YHWH speaking through Israel to the gentiles exhorting them to convert to YHWH. Hence it is an exhortation to the heathens to sing a new song, a song they have not sung before, i.e. a song in praise to YHWH.
Notice the parallelism here?
O sing unto the LORD a new song:
sing unto the LORD, all the earth.
Notice the parallelism here? Notice how it is developing what they are to do?
Sing unto the LORD, bless his name;
shew forth his salvation from day to day.
Declare his glory among the heathen,
his wonders among all people.
Now the reason.
For the LORD is great, and greatly to be praised:
he is to be feared above all gods.
For all the gods of the nations are idols:
but the LORD made the heavens.
Honour and majesty are before him:
strength and beauty are in his sanctuary.
Back again to exhortation.
Give unto the LORD, O ye kindreds of the people,
give unto the LORD glory and strength.
Give unto the LORD the glory due unto his name:
bring an offering, and come into his courts.
O worship the LORD in the beauty of holiness:
fear before him, all the earth.
Say among the heathen that the LORD reigneth:
the world also shall be established that it shall not be moved:
he shall judge the people righteously.
Back again to exhortation. Notice the repetition of judgment?
Let the heavens rejoice, and let the earth be glad;
let the sea roar, and the fulness thereof.
Let the field be joyful, and all that is therein:
then shall all the trees of the wood rejoice
Before the LORD: for he cometh,
for he cometh to judge the earth:
he shall judge the world with righteousness,
and the people with his truth.