A testament (in the sense of a “last will and testament”) only takes effect when the person who made the testament dies. Therefore Jesus had to die for the testament – the covenant – to take effect.
Clearly, death was necessary to the Old Covenant. Virtually every part of the sacrificial system under the Law of Moses was touched by blood in some way or another.
This is a foundational principle of God’s dealings with men. Modern people think that sin is remitted (forgiven) by time, by our good works, by our decent lives, or by simply death. But there is no forgiveness without the shedding of blood, and there is no perfect forgiveness without a perfect sacrifice. (Guzik)
“If there be a question about whether a man is alive or not, you cannot administer to his estate, but when you have certain evidence that the testator has died then the will stands. So is it with the blessed gospel: if Jesus did not die, then the gospel is null and void.” (Spurgeon)