The Law, or God’s rules and commands, are to point out what is right and what is wrong. It shows us that we’re wrong, and that we deserve punishment for falling short of God’s standard. We can’t keep the Law, so the Law cannot save us.
Grace, or God’s forgiveness open to us in spite of our failure, is to save us from the ultimate punishment of falling short. We don’t have to be separated from God because of our own natural failure. God can save us from that, giving us Grace through the work of Jesus when He came to fulfill the Law that we could not (Matthew 5:17; Romans 10:4).
Obeying the Law will not save you. Grace will bring you where you cannot reach. Grace brings you out of the Law’s bondage and brings you to Christ (Galatians 3:21-26).
But just because you have Grace doesn’t mean you can go and do whatever you want without regard to God’s rules. Grace was offered to you because of love, and when you accept it you return the love, and if you love God, you’ll do what He says (John 14:15; 1 John 2:3-5 & 5:3). Being more able to do what is right and being more willing to do what is right, these are both evidence of the Grace you received (1 John 1:6-7 & 3:24). (See also Rules and Relationships)
But just because obeying God is part of the evidence of Grace doesn’t mean that obeying it gives you more Grace. The whole idea of Grace means that you can’t earn it (Ephesians 2:8-10; Galatians 2:16-21). When God gives you Grace, He gives you all of it. How else are you supposed to be brought near to God? All of us need all of it!
Grace does even more! Have a look at Sufficient Grace