Rather than add to the discussion on whether the 12 tribes are still in existence in a literal way, and as some teach have settled in the UK and US, I want to state what I think the Bible says about who the True Israelites are.
What I am sharing is not replacement theology, since I believe Israel in its truest and purest form was never "replaced" but continued on! Let me explain.
Let's start with what Paul wrote in Romans 9:6: "It is not as if the Word of God failed. For they are not are all Israel who descended from Israel."
Paul explains and illustrates this point in Romans 11 by stating that God did not choose Ishmael, but Isaac, and that God did not elect or choose Esau but Jacob. Here Paul goes back into the Old Testament to prove that "they are not all Israel who descended from Israel". Even though they were direct descendents of Abraham, Ishmael and Esau became enemies of Israel. Being biologically Hebrew did not save them. And that is what we hear John the Baptist and Jesus saying to the Jews in their day. See Matt. 3:9 and John 8 for examples. In essence they preached, 'don't think because you can trace your lineage to Abraham, it will save you.'
When Jesus came, He came to seek and save the lost sheep of the House of Israel. All true Israelites were gathered to Him. All who believed and received Him were chosen by God to continue on as Israel. Notice these texts:
Phil. 3:3 "We are the true circumcision."
Gal. 6:15,16 "Neither circumcision or uncircumcision is anything, but a new creature. And those who walk by this rule, peace and mercy be upon them...and upon the Israel of God."
Gal.3:29 "And if you belong to Christ THEN you are Abraham's offspring, heirs according to the promise."
Rom. 2:29 "But he is a Jew who is one inwardly; and circumcision is that which is of the heart, by the Spirit and not by the letter..."
That was from Paul. John teaches the same thing...
Rev. 2:9 "I know your tribulation and poverty (but you are rich), and the blasphemy of those who say they are Jews and are not, but are a synagogue of Satan." (Reminds me of what Jesus said to the Jews in John 8, that their father was not Abraham but Satan!)
Rev. 3:9 "Behold, I will cause those of the syhnagogue of Satan, who say they are Jews, and are not, but lie -behold, I will make them to come and bow down at your feet and to know that I have loved you."
And Peter agrees with Paul and John...
1Peter 2:4-10 "4 Coming to Him as to a living stone, rejected indeed by men, but chosen by God and precious, 5 you also, as living stones, are being built up a spiritual house, a holy priesthood, to offer up spiritual sacrifices acceptable to God through Jesus Christ. 6 Therefore it is also contained in the Scripture,
“ Behold, I lay in Zion
A chief cornerstone, elect, precious,
And he who believes on Him will by no means be put to shame.”
7 Therefore, to you who believe, He is precious; but to those who are disobedient,
“ The stone which the builders rejected
Has become the chief cornerstone,”
“ A stone of stumbling
And a rock of offense.”
They stumble, being disobedient to the word, to which they also were appointed.
9 But you are a chosen generation, a royal priesthood, a holy nation, His own special people, that you may proclaim the praises of Him who called you out of darkness into His marvelous light; 10 who once were not a people but are now the people of God, who had not obtained mercy but now have obtained mercy.
My conclusion from these texts is that the Jews who came to Jesus and those who were saved at Pentecost were ALL Jews. These Jews who accepted their Messiah became the true Jews, God's chosen people. This became evident when God allowed Jerusalem to be completely destroyed in AD70.
Jesus called out whosoever would come to continue on as True Israelites. These "called out ones" (ekklesia) continued on as the Israel of God. Notice they were all biologically Jews to begin with. Then God commanded them to go to the gentiles and bring them into the Israel of God (Gal. 6:16). I'll conclude with a passage that sums it up beautifully:
Ephesians 2:11-22 11 Therefore remember that you, once Gentiles in the flesh—who are called Uncircumcision by what is called the Circumcision made in the flesh by hands— 12 that at that time you were without Christ, being aliens from the commonwealth of Israel and strangers from the covenants of promise, having no hope and without God in the world. 13 But now in Christ Jesus you who once were far off have been brought near by the blood of Christ.
14 For He Himself is our peace, who has made both one, and has broken down the middle wall of separation, 15 having abolished in His flesh the enmity, that is, the law of commandments contained in ordinances, so as to create in Himself one new man from the two, thus making peace, 16 and that He might reconcile them both to God in one body through the cross, thereby putting to death the enmity. 17 And He came and preached peace to you who were afar off and to those who were near. 18 For through Him we both have access by one Spirit to the Father.
19 Now, therefore, you are no longer strangers and foreigners, but fellow citizens with the saints and members of the household of God, 20 having been built on the foundation of the apostles and prophets, Jesus Christ Himself being the chief cornerstone, 21 in whom the whole building, being fitted together, grows into a holy temple in the Lord, 22 in whom you also are being built together for a dwelling place of God in the Spirit."
There are many who believe that God still plans to reconstitute the nation of Israel and rebuild a literal temple. I believe this is a false teaching. God's plan for the Jew is that they come to faith and believe in His Son, for He is able to graft in the original olive branches. The Jews in Palestine today and in the whole world for that matter are not God's chosen people. God's chosen people are those who put their faith in Jesus.
The unconverted Jew is of course beloved for their fathers sakes and God is doing all He can to save them still. The Messianic movement of our generation is one of the strongest proofs that God is about to end history. His arms are outstretched lovingly and graciously to receive them if they will only come. Our mission is to "call out" the Jew from secular Israel and come to the Jerusalem above (Gal. 4:26 and Hebrews 12:22 "But you have come to Mount Zion and to the city of the living God, the heavenly Jerusalem, to an innumerable company of angels, 23 to the general assembly and church of the firstborn who are registered in heaven, to God the Judge of all, to the spirits of just men made perfect, 24 to Jesus the Mediator of the new covenant, and to the blood of sprinkling that speaks better things than that of Abel. 25 See that you do not refuse Him who speaks. For if they did not escape who refused Him who spoke on earth, much more shall we not escape if we turn away from Him who speaks from heaven...")