1 A new song is appropriate because the Lord is constantly intervening in the world as its just king. See Ps 96:1.
2 The perfect verbal forms in vv. 1–3 are understood here as describing characteristic divine activities. Another option is to translate them as present perfects, “has performed … has accomplished deliverance, etc.” referring to completed actions that have continuing results.
3 Heb “his right hand delivers for him and his holy arm.” The right hand and arm symbolize his power as a warrior-king (see Isa 52:10). His arm is “holy” in the sense that it is in a category of its own; God’s power is incomparable.

In other versions

A Psalm.

Oh sing to the Lord a new song,

for he has done marvelous things!

His right hand and his holy arm

have worked salvation for him.

A psalm.

Sing to the Lord a new song,

for he has done marvelous things;

his right hand and his holy arm

have worked salvation for him.

A psalm.

Sing a new song to the Lord,

for he has performed wonders;

his right hand and holy arm

have won him victory.

A psalm.

Sing a new song to the Lord,

for he has done wonderful deeds.

His right hand has won a mighty victory;

his holy arm has shown his saving power!

A psalm.

Sing to Yahweh a new song, for he has done wonders.

His right hand and his holy arm have secured his victory.

A Psalm.

O sing unto the Lord a new song;

For he hath done marvellous things:

His right hand, and his holy arm, hath gotten him the victory.

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