Without an understanding of the Old Testament and the Jewish construct, many of the references and allusions in the New Testament would be difficult to understand.
For example, the New Testament often references and builds upon the teachings and prophecies of the Old Testament, such as the coming of a Messiah and the promised salvation for humanity. In this week's reading overview of Luke, the authors tell how “Luke seems to arrange his Gospel account around one dominating theme: Jesus accomplishes the fulfillment of God’s salvific promises.” (Dottie Rhoads, 2022) Without knowing the promises of salvation and the covenant with Abraham, one would not understand the impact of this statement.
Another example would be the statement Jesus makes in Mark 10:25 of the NIV “It is easier for a camel to go through the eye of a needle than for someone who is rich to enter the kingdom of God.” In western culture we picture a camel going through the eye of a sewing needle, when in fact this references a doorway.
The person passing through the small opening would have to unload their camel and dismount, leaving them vulnerable to attack and therefore minimizing the threat. (Paul Bergen, TBCO) Where the Western reference would mean that it is clearly impossible for a rich man to enter the gates of heaven, the context in 60 AD meant that he would have to unload everything and make himself vulnerable to God in order to know the Kingdom of God. It would be difficult, but not impossible.
In short, the New Testament cannot be fully understood without the context of the Old Testament, as it is the foundation for the theology, history, and cultural background in which the New Testament was written.