What is the point with the Old Testament?

With the understanding of our New Covenant in Christ, many people question the role of the Old Testament in Christianity.
The answer to this pertinent question can be captured in Paul’s challenge to Timothy,

[do] your best to present yourself to God as one approved by him, a worker who has no need to be ashamed, rightly explaining the word of truth. (2 Tim. 2:15)

At the time of writing, Christianity was still at its formative state, hence there was no text known as the New Testament. Clearly this admonition was for the study of the Torah, Mishnah, Midrash, and other classical Jewish writings.
Paul himself had studied under Gamaliel, a known Rabbi with intellectual lineage to back his teaching and worldview. With a view to assert his authority, Paul gives us a preview of his credentials when he notes,

“I am a Jew, born in Tarsus of Cilicia,but brought…