to fulfill the word that is written in their law

You can translate this in an active form. "Word" here is a metonym for the entire message of God. Alternate translation: "to fulfill the prophecy in their law" (See: rc://en/ta/man/jit/figs-activepassive and rc://en/ta/man/jit/figs-metonymy)

law

This refers generally to the entire Old Testament, which contained all of God's instructions for his people.