The Old Covenant - the agreement between God and ancient Israel - was a "guardian" or "custodian" for the children of Israel. It provided a means by which the Israelites could have health and wealth and many of the good things this life has to offer - if they would have followed the laws contained within that covenant. For example, the law of the Sabbath has tremendous physical benefits, for man, animals, and even the land. The law of tithing teaches good financial handling, and when it is done in faith it ensures financial stability. The laws which were a part of the covenant agreement would have kept Israel heading in the right direction, and would have helped prepare a people who should have recognized and accepted their rightful Ruler when He was born a man - except their hearts were not changed. God wants a change of action that proceeds from a change of heart - not a change of action just for the sake of the action.
The Old Covenant was a legitimate system, ordained by God, with fantastic physical benefits - if Israel had obeyed. That contractual agreement was meant to be a means to an end, and not the end in itself. It was meant to teach the people and hedge them in, to prepare them for the next stage of their existence - just like a guardian teaches and prepares a child to take over a business or inherit an estate. The covenant - not God's holy, spiritual law - was a step in the process, but that agreement became obsolete when the Master arrived and began His instruction. However, many of the laws contained within that covenant pre-dated the agreement with Israel, and thus are just as relevant today as they were for Israel.
Even though God's law is eternal and thus still required to be kept, justification has always been by faith. Abraham was justified by faith, even though God says he also "obeyed My voice and kept My charge, My commandments, My statutes, and My laws." (Genesis 26:5) His obedience to God's law did not justify him, for his obedience was not perfect. Justification has always been on the basis of faith, because the instant a man sins - as all men have (Romans 3:23) - it becomes impossible to come before God on the basis of sinless perfection. Faith in the Savior is thus required for justification, and the law then lights the path the repentant and justified sinner must walk in order to keep from sinning further.
The Old Covenant was a system ordained by God to include His "royal law" (James 2:8) for the purpose of teaching Israel how to live. Even though the Old Covenant is obsolete, that same royal law is at the core of the New Covenant (Hebrews 8:7-13) because it teaches us how to live. But since we have transgressed that law, faith in the Savior is required for our sins to be forgiven and for us to be justified before God.