You can find a YouTube playlist here with many of the songs suggested below.
Gathering
The final Sunday of the Christian year celebrates the Reign of Christ or Christ the King Sunday and there are many gathering songs you could use which pick up this theme. There are some great songs inspired by the psalms such as O worship the King all glorious above (CH 127), The Lord is King lift up your voice (CH 129 / MP 656) and Clap your hands, all you nations (PFAS 47D / GSW 15), a joyous setting of Psalm 47 from West Africa which would be very easy to pick up. You could also consider classic hymns such as Rejoice! the Lord is King (CH 449 / MP 575) and Jesus shall reign where’er the sun (CH 470 / MP 379) or Come people of the risen King (MP 1267 / CCLI / Getty) for a contemporary hymn. Some possible worship songs could be My Jesus, my Saviour / Shout to the Lord (CH 531 / MP 1003 / CCLI), High praise (CCLI) or Come and worship Christ the King (Resound).
Word
Psalm 132 is one of the psalms few writers have tackled but for metrical options you could use either When David had a longing (PFAS 132A) and Remember Lord for David (CCLI), both written to be sung to Thaxted. Arise, O King of grace, arise (O Saviour come) (Scheer) is a setting of words by Isaac Watts with an added chorus and a Christological emphasis that makes it particularly appropriate for celebrating the Reign of Christ.
Response
You could use many of the songs suggested for Gathering or Sending to link to the Gospel. Meekness and majesty (CH 356 / MP 465) and You, Lord, are both Lamb and Shepherd (CH 355) both touch on Jesus being human and divine with his kingdom not of this world. The head that once was crowned with thorns (CH 438 / MP 647), All hail King Jesus (CCLI) and King of kings (CCLI) all link us to the Holy Week context of the reading while King of kings majesty (MP 1000 / CCLI) could be use as a more straightforward song of praise. The kingdom of God is justice and peace (Taizé) and God our Father (Let your Kingdom come) are more reflective songs which could fit, including as a prayer response (just using the chorus of the latter).
While we don’t want to preempt Advent 1C next week, there is an overlap here with the reference to Jesus coming with the clouds and some of the same songs would link such as Lo, he comes with clouds descending (CH 477 / MP 424) and Days of Elijah (MP 1012 / CCLI). There is a credal feel to the opening of the reading with the statements of who Jesus is which could resonate with This I believe (The Creed) (CCLI) or Cornerstone (CCLI). You could link to the final verse with Alpha and Omega (CCLI), a song from Zimbabwe which has become popular as a worship song.
The morning imagery of the Old Testament could suggest Christ, whose glory fills the skies (CH 578 / MP 79) or God of the Bible (Fresh as the morning) (MV 28), a wonderful song that isn’t well known in the UK but with a chorus that captures the essence of v4 while also linking to God’s covenant. Hail to the Lord’s anointed (CH 474 / MP 204) would make an explicit link between David and Christ as well as giving a nod towards Advent. As well as the German chorale melody there is a version of the latter for band set to a traditional Irish melody by New Scottish Hymns (New Scottish) and a new version by Indelible Grace (link).
Sending
You could finish by singing praise to Christ the King with hymns such as Crown him with many crowns (CH 459 / MP 109), Christ triumphant, ever reigning (CH 436 / MP 77) and How shall I sing that majesty (CH 128). Alternatively, you could focus more on our calling with worship songs such as Hear the call of the kingdom (MP 1282 / CCLI / Getty), Build your kingdom here (CCLI) and Let your kingdom come (CCLI) or short songs such as Sent by the Lord am I (CH 250) and Sizohamba naye / We will walk with God (CH 803).