Hebrews 8

In that He says, “A new covenant,” He has made the first obsolete. Now what is becoming obsolete and growing old is ready to vanish away. v.13

Read chapter 8
At this point in history, after Jesus Christ had died and resurrected, the law of the old covenant through Moses was still going on.  Jesus' time on earth did not stop the law from being upheld rather He fulfilled the law.  It changed in the period of the book of Acts from  a "have to" to a "continue to do what you are able to do."  We see clearly throughout the book of Acts of Paul and other believing Jews still upholding the law.  We notice in this chapter of Hebrews, which was written during this period of Acts, that this old covenant was becoming obsolete, meaning it was still there but waxing away and soon at the change of the Acts period it would be obsolete.  Understanding that the law was still being upheld during this time by God's commissioned men, help us to understand that dispensation and the change that took place afterwards in the dispensation we live in today.  
This new covenant mentioned here is what we read about in Jeremiah 31, but we still await for that to be in effect when God's Kingdom comes.  For now, the day we live in neither Jew nor Gentile live under one of these covenants, for we all live under grace.  Yet oh how we crave for the terms of the new covenant to rule where God's law wont just be a book that men have to teach and implement on others, but where it will be written on everyones heart.  This is the better covenant established on better promises (v.6).  Take heart, the world we live in today isn't it, there's still more to come and it is so much better!