What gives unity to New Testament and Old Testament?

Answer 1

The answer is not what but who and that who is Jesus Christ; he is the cornerstone; the central theme around which the Bible is centered; "the lamb for sinners slain". The Old Testament believers such as Abel; Abraham; Moses; David and many more all put their trust in their belief that their right to approach God was only through a blood sacrifice (sheep; goats; cattle).
By doing so they were unknowingly rolling their sin forward until the true sacrifice for sin could be offered- Jesus Christ. Where as they unknowingly looked forward to the true sacrifice that takes away the sin of the world; we today of the New Testament knowingly look backward and put our trust in Calvary's blood sacrifice for us.
Heb 10: 4] For it is not possible that the blood of bulls and of goats should take away sins. [19] Having therefore, brethren, boldness to enter into the holiest by the blood of Jesus
The Old Testament law of Moses was to keep us focused on the theme and need of blood sacrifice and to teach us what was right and wrong so we would recognize sin and offer a blood sacrifice
I John [2] And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world.
His blood sacrifice is the hope and also the ground upon which all may have fellowship with God; those past; present and future.