There is a lot to study about the "old" and "new" the covenants. I have summed it up this way:
Hebrews 10:16 This [is] the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them; 10:17 And their sins and iniquities will I remember no more.
If God were speaking to us today of the same covenant, perhaps it would be something like this:
Look, I understand that life on this earth is full of problems. From the day that sin entered, all have sinned and brought terrible curses—consequences—upon themselves and others. Your lives are miserable, and all you have to look forward to is death. BUT I extend to you the same proposition that I have extended from the very first. My covenant: A promise of life—blessings!
My Son—Jesus Christ, Creator of the Universe, my other self—actually came to this earth, died the death that was yours so you can live eternally with me. If you accept, I will send the Holy Spirit to teach you how to walk in this sinful world and give you the overcoming power so you can avoid the consequences of sin and can sit down with Me on My Throne
The journey will not be easy. In fact we are told we will. 1 Peter 1:7 tells us we will have troubles, "That the trial of your faith, being much more precious than of gold that perisheth, though it be tried with fire, might be found unto praise and honour and glory at the appearing of Jesus Christ: " But in the end the promise of Revelation in 3:21 is ours. To him that overcometh will I grant to sit with me in my throne, even as I also overcame, and am set down with my Father in his throne.
Just writing this out helped me. Let me know if it helped you.