Revelation 14:3

They sang
ἄδουσιν [adousin] , present tense, they are singing. Isaiah indicated that the ransomed (redeemed , below) would return to Zion with singing (Isa. Isa. 35:10; Isa. 51:11). Those who have been redeemed from amidst great difficulty respond with songs of great praise. “For the LORD has redeemed Jacob, and ransomed him from the hand of one stronger than he. Therefore they shall come and sing in the height of Zion” (Jer. Jer. 31:11-12). If the harpists are the singers in heaven, then they sing in commemoration of the unique experience of the 144,000 on earth. If the 144,000 are singing in heaven, the song they sing is probably motivated by their similar experience to those who had victory over the Beast through martyrdom (Rev. Rev. 15:3+). Or, if this is a millennial scene and they sing from the earth, they sing because they were protected for the entire duration of the Tribulation. God brought them “through the sea” as when Israel was pursued by Pharaoh:

So the Lord saved Israel that day out of the hand of the Egyptians, and Israel saw the Egyptians dead on the seashore. Thus Israel saw the great work which the Lord had done in Egypt; so the people feared the Lord, and believed the Lord and His servant Moses. Then Moses and the children of Israel sang this song to the Lord, and spoke, saying: “I will sing to the Lord, for He has triumphed gloriously! The horse and its rider He has thrown into the sea!” (Ex. Ex. 14:30-Ex. 15:1)

See commentary on Revelation 14:1. a new song
The twenty-four elders, probably representatives from among the Church, “sang a new song” (Rev. Rev. 5:9+). The subject of their song was redemption (Rev. Rev. 5:8-10+). Here we see one of the purposes of trials and tribulations—to produce in us a new song of praise to God (Ps. Ps. 40:3; Ps. 98:1; Ps. 144:9). These new songs often express themes of redemption and salvation. “The song is that of victory after conflict with the dragon, beast, and false prophet: never sung before, for such a conflict had never been fought before; therefore new.”¹ as it were
This phrase is missing from the MT text and about half of the manuscripts which contribute to the NU text. before the throne
Which throne is this? The nearest previous mention of a throne related to God is His throne in heaven to which the child was caught up (Rev. Rev. 12:5+ cf. Rev. Rev. 1:4+; Rev. 3:21+; Rev. 4:2-10+; Rev. 5:1+, Rev. 5:6-7+, Rev. 5:11-13+; Rev. 6:16+; Rev. 7:9-17+; Rev. 8:3+). Every other mention of a throne in conjunction with the living creatures and elders is the Father’s throne in heaven (Rev. Rev. 5:6+, Rev. 5:11+; Rev. 7:11+; Rev. 14:3+; Rev. 19:4+). before the four living creatures
These are the four ζῳˊων [zōōn] , “living ones,” who attend the throne in heaven (Rev. Rev. 4:6+, Rev. 4:8-9+; Rev. 5:6+, Rev. 5:8+, Rev. 5:11+, Rev. 5:14+; Rev. 6:1+, Rev. 6:6+; Rev. 7:11+; Rev. 8:9+; Rev. 14:3+; Rev. 15:7+; Rev. 19:4+). See commentary on Revelation 4:6. and the elders
The twenty-four elders who sit on thrones before the Father’s throne. See commentary on Revelation 4:4. and no one could learn that song
Why could no one else learn the song?² We suggest that the song is highly personal to the experiences of these 144,000 Jewish evangelists from the time of the Tribulation. In the same way that the twenty-four elders could sing the song of redemption: “For you were slain, and have redeemed us to God by Your blood out of every tribe and tongue and people and nation, and have made us priests to our God; and we shall reign on the earth,” [emphasis added] only these men could sing about the keeping power of God that these had experienced. “Only those who had gone through that Tribulation could understand the song which celebrated it.”³ Those who have been forgiven much or have endured intense danger and persecution are best able to appreciate the gifts of God which many others take for granted. Without such experiences, we tend more toward Simon the Pharisee than the woman who washed Jesus’ feet with her tears (Luke Luke 7:36-48). Are you going through immense hardships? Remember that God is sovereign and every tear you shed will surely contribute toward His glory and your subsequent ministry to others (Rom. Rom. 8:28). who were redeemed
οἱ ἀγορασμένοι [hoi agorasmenoi] , perfect passive participle, the ones having been purchased. Prior to Jeremiah’s presentation of the New Covenant to Israel (Jer. Jer. 31:31), he relates a time when God promises to save the remnant of Israel and gather them to Mount Zion. He refers to His gathered flock as the redeemed of Jacob, those who were ransomed (Jer. Jer. 31:6-13). Their return will be accompanied by rejoicing and singing. This is not to be spiritualized as applying to the general family of faith, it is Jacob who is the object of these promises. Isaiah also indicates the power of redemption as fuel for praise: “And the ransomed of the LORD shall return, And come to Zion with singing, With everlasting joy on their heads. They shall obtain joy and gladness, And sorrow and sighing shall flee away” (Isa. Isa. 35:10 cf. Isa. Isa. 51:11).

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Notes

¹ A. R. Fausset, “The Revelation of St. John the Divine,” in Robert Jamieson, A. R. Fausset, and David Brown, A Commentary, Critical and Explanatory, on the Old and New Testaments (Oak Harbor, WA: Logos Research Systems, Inc., 1997, 1877), Rev. 14:3.

² “During the time of the First and Second Temples, a number of the Levites played on two types of harps, singing arcane melodies that no one else was permitted to learn. This knowledge was passed from father to son, until the destruction of the Second Temple.”—Randall Price, The Coming Last Days Temple (Eugene, OR: Harvest House Publishers, 1999), 390.

³ E. W. Bullinger, Commentary On Revelation (Grand Rapids, MI: Kregel Publications, 1984, 1935), Rev. 14:3.