Jesus is not only Lord, but KING! He is the head of all rulers and Kings having complete dominion at the time of the writing and all of the future.

1:19and what is the immeasurable greatness of his power toward us who believe, according to the working of his great might 20that he worked in Christ when he raised him from the dead and seated him at his right hand in the heavenly places, 21far above all rule and authority and power and dominion, and above every name that is named, not only in this age but also in the one to come. 22And he put all things under his feet and gave him as head over all things to the church,

We, as the church are seated with Him ruling and reigning with Him was well.

1:3 Blessed be the God and Father of our Lord Jesus Christ, who has blessed us in Christ with every spiritual blessing in the heavenly places
2:6 and raised us up with him and seated us with him in the heavenly places in Christ Jesus,
The promises of the covenant are applied literally to Gentiles within the Church.
2:10For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them.
11Therefore remember that at one time you Gentiles in the flesh, called "the uncircumcision" by what is called the circumcision, which is made in the flesh by hands-- 12remember that you were at that time separated from Christ, alienated from the commonwealth of Israel and strangers to the covenants of promise, having no hope and without God in the world.

The removal of the distinction of the Jew and Gentile is stressed!

2:12remember that you were at that time separated from Christ, alienated from the commonwealth of Israel and strangers to the covenants of promise, having no hope and without God in the world. 13But now in Christ Jesus you who once were far off have been brought near by the blood of Christ. 14For he himself is our peace, who has made us both one and has broken down in his flesh the dividing wall of hostility 15by abolishing the law of commandments and ordinances, that he might create in himself one new man in place of the two, so making peace, 16and might reconcile us both to God in one body through the cross, thereby killing the hostility. 17And he came and preached peace to you who were far off and peace to those who were near. 18For through him we both have access in one Spirit to the Father. 19So then you are no longer strangers and aliens, but you are fellow citizens with the saints and members of the household of God

The building up of the Church is referred to as the building up of the Temple.

2:20built on the foundation of the apostles and prophets, Christ Jesus himself being the cornerstone, 21in whom the whole structure, being joined together, grows into a holy temple in the Lord. 22In him you also are being built together into a dwelling place for God by the Spirit

The New Testament Church is claimed to have been taught in the Old Testament, just not as clearly.

3:1For this reason I, Paul, a prisoner for Christ Jesus on behalf of you Gentiles-- 2assuming that you have heard of the stewardship of God's grace that was given to me for you, 3how the mystery was made known to me by revelation, as I have written briefly. 4When you read this, you can perceive my insight into the mystery of Christ, 5which was not made known to the sons of men in other generations as it has now been revealed to his holy apostles and prophets by the Spirit. 6This mystery is[a] that the Gentiles are fellow heirs, members of the same body, and partakers of the promise in Christ Jesus through the gospel.

Christís Kingly enthronement is celebrated by the pouring out of gifts upon His Church/Kingdom.

4:8Therefore it says,
"When he ascended on high he led a host of captives, and he gave gifts to men."
9(In saying, "He ascended," what does it mean but that he had also descended into the lower parts of the earth? 10He who descended is the one who also ascended far above all the heavens, that he might fill all things.) 11And he gave the apostles, the prophets, the evangelists, the pastors and teachers

Paul teaches that the Kingdom is spiritual rather than Political.

5:5For you may be sure of this, that everyone who is sexually immoral or impure, or who is covetous (that is, an idolater), has no inheritance in the kingdom of Christ and God.