Is there a contradiction between 1 Corinthians 15:24-28 and Daniel 7:13-14, Luke 1:33, and Ephesians 1:21?

1 Corinthians 15:24-28 states that Jesus will reign only until all enemies have been placed under His feet, at which point He will hand everything to the Father and subject Himself to Him.

No. 1 Corinthians 15:24-28 echoes the same theme as other biblical passages in the same vein:

^{1 Corinthians 11:3} the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God.

Compare the above, with the verse you've just quoted:

^{1 Corinthians 15:28} When all things are subjected to Him, then the Son Himself will also be subjected to the One who subjected all things to Him, so that God may be all in all.

Both speak of hierarchical chains:

• wife - husband - Christ - God
• creation - Son - God

Op asks: Is there any way to resolve this apparent contradiction between the verses listed above?

The reign of Christ is for the eons, or ages. It's for a very long but limited period of time.
This will be when He reigns as God's son.

and unto the Son: 'Thy throne, O God, is to the age of the age; a sceptre of righteousness is the sceptre of thy reign. Hebrews 1:8 YLT

Prior to the eon of the eon he will be reigning in the 1000 year as King over Israel.

"During the millennium, Jesus will reign as king over Israel and all the nations of the world (Isaiah 2:4; 42:1). The world will live in peace (Isaiah 11:6–9; 32:18), Satan will be bound (Revelation 20:1–3), and, at the beginning, everyone will worship God (Isaiah 2:2–3). The purpose of the 1,000-year reign is to fulfill various promises God made to the world. Some of these promises, called covenants, were given specifically to Israel. Others were given to Jesus, the nations of the world, and creation. Jesus’ 1,000-year reign will be a time of promises kept". Quoted from Got questions.

There will come a time when everything will be subjected to Christ. After all rule and authority has been abolished, including death, Christ hands the kingdom to God the Father.

For it behooves Him to reign until He shall have put all the enemies under His feet. 26The last enemy to be abolished is death. 27For “He has put in subjection all things under His feet.”b But when it may be said that all things have been put in subjection, it is evident that the One having put in subjection all things to Him is excepted. 28Now when all things shall have been put in subjection to Him, then also the Son Himself will be put in subjection to the One having put in subjection all things to Him, so that God may be all in all. 1 cor. 15: 25-28

It is in Luke where we find the reign of God never ends.

and he shall reign over the house of Jacob to the ages; and of His kingdom there shall be no end.' Luke 1:33

God will have completed His goal for his entire creation. When God is all in all.
His kingdom rules in every heart. Love never fails.

No, there is no contradiction because at no point does Christ ever relinquish his Kingship. Neither is it ever taken away from him. He will hand over the completed work of his Kingdom rule to the Father at a certain point, once everything in all creation has been restored to what it originally was. This will glorify the Almighty.

When creation went askew (due to sin) the Son of God already knew his assigned role in restoring it. At a particular time in the future, the Father would send him to earth and he would willingly go, die, be resurrected then return to the Father. The Holy Spirit also knew his assigned role in the restoration. He would be sent to earth after the Christ had returned to heaven, to enable Christians to be ambassadors for Christ, until Christ returned in great glory. All three persons in the Godhead had worked out the plan of salvation before any creating started. All three were involved in the creation. All three are united in restoring everything to sinless perfection. All of this glorifies the Almighty. But to glorify the Almighty is to glorify the others in the Godhead for they are one in Deity.

The Father and the Son share the one, divine nature, with absolute unity of the Spirit in that nature. Various scriptures highlight the role of one Person at a particular time, then a different but complimentary role of another of the Person at another time.. Once you look at all the texts you have mentioned in that light, there is no contradiction.

Your assumption that "Jesus will reign only until all enemies have been placed under His feet" is not correct. Jesus's reign is forever, a truth to which the scriptures you cited attest. Here is another scripture that attests to the eternal reign of Jesus Christ:

The seventh angel sounded his trumpet, and there were loud voices in heaven, which said: “The kingdom of the world has become the kingdom of our Lord and of his Messiah, and he will reign for ever and ever" (Revelation 11:15)

When (or after) Jesus has "abolished all rule and authority and power" and "put all his enemies under his feet," including death, only then will he hand over the kingdom to God the Father" (1 Corinthians 15:24). Moreover, Paul adds, "the Son himself will be made subject to him who put everything under him, so that God may be all in all" (ibid., v.28, my emphasis).

In other words, there will never come a time when "everything" is not under the Son.

Neither verse 24 nor verse 28 teaches that Christ will be dethroned. His reign is indeed forever. By the same token, however, in his reign, Jesus will be subject to his Father who has put everything under his Son. To be subject to his Father, Jesus is in no way stepping down from his eternal throne, nor is he in any way relinquishing any of his attributes as God the Son, including omnipotence.

The eternal order has been, is now, and forever will be: Father, Son, and Holy Spirit. Within that divine order, there is perfect equality among the three persons of the Trinity. Each person in the Godhead, however, has an eternal role to play. In very human terms, which I use reverently, God the Father has delegated tasks to his well-beloved Son, with whom he is well pleased (see Matthew 3:17; 17:5; Mark 1:11; 9:7; Luke 3:22; 9.35; and 2 Peter 1:17).

In the human sphere, particularly in the workplace, we sometimes assume that the employee is somehow less than, or inferior to, the employer. After all, the employer signs the paychecks, and the "boss" has more power than the people who "report to" her or him. He or she has the authority to dismiss an employee for any reason.

Not so in the divine sphere. The Father is the Sovereign LORD (YHWH). The Son, the Second Person of the Trinity, is subject to the Father and is perfectly obedient to him (see John 8:29). There is a mutual love affair, so to speak, between Father and Son. The Father loves his Son, and the Son loves his Father.

The Holy Spirit's role seems to be to reveal Jesus to all created beings, particularly to true believers in Jesus (see John 14:15 ff.) Jesus called him "the Spirit of truth" (ibid., v.17). So, Jesus IS the truth, and the Spirit of truth reveals him to people. The Holy Spirit who indwells each and every believer in Jesus Christ is Christ's presence with them. He is the Paraclete who teaches them, comforts them, helps them to pray, and empowers them to manifest the Fruit of the Spirit. In so doing, He enables Christians to become more like Christ.

I'll conclude my remarks by providing you with the words of the Isaac Watts hymn, "Jesus Shall Reign":

Jesus shall reign where’er the sun
Does its successive journeys run;
His kingdom stretch from shore to shore,
Till moons shall wax and wane no more.

To Him shall endless prayer be made,
And praises throng to crown His head;
His name like sweet perfume shall rise
With every morning sacrifice.

People and realms of every tongue
Dwell on His love with sweetest song,
And infant voices shall proclaim
Their early blessings on His name.

Blessings abound where’er He reigns:
The pris’ners leap to lose their chains,
The weary find eternal rest,
And all who suffer want are blest.

Let every creature rise and bring
The highest honors to our King,
Angels descend with songs again,
And earth repeat the loud amen.