1 Peter 1:11
Searching what, or what manner of time the Spirit of Christ which was in them did signify, when it testified beforehand the sufferings of Christ, and the glory that should follow. (KJV)
The fact that this verse says the “spirit of Christ” was upon people in the Old Testament has caused people to believe that Christ himself was present in the Old Testament. But, as we will see, such is not the case. In the first place, the phrase “spirit of Christ” never appears in the Old Testament. The “spirit of the Lord” or “the spirit of God” appears over and over, but never the “spirit of Christ.”
The spirit that God places upon people takes on different names as it refers to different functions. This can be abundantly proven. Nevertheless, the spirit is the same. God always gives His spirit, and then it is named as it functions. When it is associated with wisdom, it is called the “spirit of wisdom” (Ex. 28:3; Deut. 34:9; Eph. 1:17). When it is associated with grace, it is called the “spirit of grace” (Zech.12:10; Heb. 10:29). When it is related to glory, it is called the “spirit of glory” (1 Pet. 4:14). It is called the “spirit of adoption” when it is associated with our everlasting life (Rom. 8:15, which is translated as “spirit of sonship” in some versions). It is called “the spirit of truth” when it is associated with the truth we learn by revelation (John 14:17; 16:13). When it came with the same power as it brought to Elijah, it was called “the spirit of Elijah” (2 Kings 2:15). These are not different spirits. All the names refer to the one gift of holy spirit that God gives. Ephesians 4:4 states clearly that there is “one spirit,” and that spirit is God’s gift of holy spirit given to some people in the Old Testament and to all believers today.
When Peter mentions that “the spirit of Christ” was upon prophets as they “predicted the sufferings of Christ and the glory that would follow,” it is easy to see that the spirit is called the “spirit of Christ” because it is associated with Christ and foretold of Christ, not because Christ was actually alive during the Old Testament.
Racovian Catechism, pp. 146-148