Wherever we find the words - "new song" we have seen it in the midst of salvation and redemption. But in this passage it goes a bit beyond that. " . . . and they were singing a new song before the throne and before the four living creatures and before the elders. No one could learn that song except the 144,000 who had been redeemed from the earth." Here again it is present tense - they are singing. Isaiah indicated that the ransomed would return to Zion with singing. Those who have been redeemed from amidst great difficulty always respond with songs of praise!
But here in this passage as a whole we see not only the new song of redemption. We see also that one of the purposes of trials and tribulations is to produce in us a "new song" to praise to God. This song here is that of victory after conflict with the dragon, beast, and false prophet sung as never before because such a conflict had never been seen.
Those who have been forgiven much and have gone through and endured trouble and persecution are able to better appreciate the gifts of God while others sometimes take them for granted. We have to remember that God is Sovereign and every tear you shed contributes toward His glory and your enabled ministry to others.
In Him, sorrow and sighing give way to singing the "new song" in joy! mjm