From this point on, the true and living God is the God of Israel (the Jewish nation). And God deals only with His people. This doesn't mean that all was smooth sailing for the Israelites. The history of the Jews in the Old Testament is proof that they fluctuated from belief to disbelief, obedience to disobedience. Regardless, in II Samuel 7:8-16, God sent a message by Nathan to David. Long after David is dead, he will have a descendant who will have a kingdom that will last forever. He goes on to tell David that his descendant will be called God's son.
The prophesying of the kingdom and its' coming king is related in I Chronicles 17 and 22, Isaiah 9:7, Ezekiel 37:21-28, and Daniel 7:13,14. It's also spoken of by John the Baptist and others in the New Testament. It's no secret. The Jewish people have been waiting for the King and the Kingdom according to the promise of God and scripture.
Then, something happens after Jesus Christ's death, burial, and resurrection. Up until this time the message was delivered only to the Jews. John the Baptist was preaching "...the kingdom of heaven is at hand," (Matthew 3:2) and Jesus had admonished his disciples to not go into the way of the Gentiles but rather go to the lost sheep of the house of Israel (Matthew 10:5,6). But then Saul arrives on the scene in Acts 9 and has a conversion experience on the road to Damascus.
Now there is the Apostle Paul (Saul of Tarsus) going to the Gentiles. Gentiles are anyone of any nationality other than the Jew. Not a Jew?--then you're a Gentile. Paul states in Acts 13:46, 47 that the Lord commanded him to be a light to the Gentiles. The Jews became combative toward Paul but he persevered and carried his ministry to the cities of the Gentiles. The book of Acts contains most of his journeys. The remainder are in his letters.
Paul's gospel that he preached can be found in I Corinthians 15:1-4. His gospel says that Christ died for our sins, was buried and rose again the third day according to scriptures. For those who believe this with their hearts, they are saved. It's pretty plain this couldn't have been preached until after the crucifixion. So up until then, the kingdom of heaven was preached to the Jews. That's why there is no mention of it in the four gospels. Being saved is stated again in Romans 10:9.
Paul also speaks of a mystery revealed to him by God. Ephesians 3:1-12 tells us that the grace of God, his unwavering favor toward us, is all that we need. Once one is a believer (the through-and-through kind) it's grace and nothing else that saves us. A little aside here, though, the truly saved have a thirst for God and are "pressing toward the mark" as Paul says. There's a relentless desire to be more for God.
I Corinthians 12:12-27 speaks of the body of Christ and how all those who believe are members of that body. Once saved, believers become members of this body and find their place in it. The thing to remember here is that you can't have it both ways. Synagogue worship and trying to obey 613 laws do not fit with God's grace. Believing, or taking God at his word, is sufficient. Being a member of the body of Christ is all that is now required.