Christ said, "And other sheep I have which are not of this fold; them also I must bring, and they will hear My voice; and there will be one flock and one shepherd" (John 10:16).
"This fold" refers to Judah—the Jews who were living in Judea. Christ come to His own—to the Jews—and His own did not receive Him (John 1:11). Christ was born of the tribe of Judah, but the Jews rejected Him saying, "We will not have this man to reign over us" (Luke 19:14).
Who, then, are the "other sheep"? There are two legitimate answers: one physical, one spiritual.
On a physical level, the "other sheep" are the other tribes of Israel. Israel (Jacob) had more than one son—twelve in all. The "other sheep" then are the descendants of the other sons of Jacob. Christ refers to these other tribes of Israel as "the lost sheep of the house of Israel" (Matthew 10:6).
Israel and Judah became two separate nations or houses during the reign of Rehoboam, Solomon's son (see I Kings 12). The nation of Israel, the northern ten tribes, were conquered by the Assyrians in 721 BC, and many of its people were removed to the area near the Caspian Sea. Eventually, the tribes migrated from there into northwestern Europe. Thus, the "other sheep," or the lost tribes of Israel, were not in Judea during Christ's ministry.
Christ concludes by saying, "And there shall be one flock and one shepherd" (John 10:16). When will the house of Judah and the house of Israel be one flock and have one king, one shepherd? The prophet Ezekiel gives the answer (Ezekiel 37:21-28). David will be that king with Christ, the chief shepherd (verses 24-25). Ezekiel 34:23-24 and Jeremiah 30:9 show that David is to be resurrected from the dead and made king. The resurrection from the dead occurs at Christ's second coming to this earth (I Thessalonians 4:13-15; I Corinthians 15:20-23, 50-52). Christ will then establish the new covenant with the house of Israel and the house of Judah (Hebrews 8:8-10; Jeremiah 31:31-33; 50:4-5).
On a spiritual level, the "other sheep" are the members of God's church. Jesus and the apostles frequently call Christians "sheep" (e.g., Matthew 25:33; Mark 14:27; John 21:15-17; I Peter 2:25; etc.). Christ's Jewish audience did not "hear [His] voice" but instead rejected Him and His message and forced the Roman government into crucifying Him. Though many of the original members of the church were Jews, salvation was soon opened to Gentiles as well, and together they became an entirely new entity, the household of God, the church (see Ephesians 2:11-22).
Paul explains in Romans 9-11 that national Israel/Judah has been put aside for the time being for their ultimate spiritual good, and thus God's flock is presently His church. As the apostle puts it, "Israel has not obtained what it seeks [salvation and the promises of God]; but the elect [the church] have obtained it, and the rest were hardened" (Romans 11:7). Indeed, Paul names the church as "the Israel of God" in Galatians 6:16. He also shows in I Corinthians 12:12-27 and Ephesians 4:4 that there is only one body (flock), and Peter says there is only one Chief Shepherd, Jesus Christ (I Peter 5:4).