What role does the Old Testament Law have, in the life of a Christian?

So far, the story of the whole Bible has been a story of great promise in search of fulfillment. A God who makes promises to a people who break them. Right from the beginning, our human problem is sin. Sin brings death and separation (exile) from God. But so far no one has obeyed God! No-one has dealt with our sin problem.
Up until now everyone has shown themselves to be a sinner, not a Saviour.
God’s promise of a King and Saviour who deals with sin is fulfilled in the birth of a baby boy at Bethlehem (the town of David). But in another act of repeated history, God’s people reject Jesus as their King - and crucify him.
Was the death of Jesus the Messiah all in vain?

References:

• Galatians 3:1-18
• Genesis 17:1-8
• Romans 8:1-4
• Romans 8:31-39