Here is a good, concise summary of the Israel/remnant theme from a New Testament perspective:
. . . Jesus had become a remnant of one. He was the embodiment of faithful Israel, the truly righteous and suffering servant.
Unlike the remnant of the restoration period, he committed no sin (Isa. 53:9; 1 Pet. 2:22).
As the embodiment of the faithful remnant, he would undergo divine judgment for sin (on the cross), endure an exile (three days forsaken by God in the grave), and experience a restoration (resurrection) to life as the foundation of a new Israel, inheriting the promises of God afresh.
As the remnant restored to life, he becomes the focus of the hopes for the continued existence of the people of God in a new kingdom, a new Israel of Jew and Gentile alike.
As the nucleus of a renewed Israel, Christ summons the “little flock” that will receive the kingdom (Dan. 7:22, 27; Luke 12:32) and appoints judges for the twelve tribes of Israel in the new age (Matt. 19:28; Luke 22:30).
The church is viewed as the Israel of that new age (Gal. 6:16), the twelve tribes (James 1:1), “a chosen people, a royal priesthood, a holy nation, God’s special possession” (Ex. 19:6; 1 Pet. 2:9).
tgc