This video provides a helpful way of understanding what it means to be "under grace" by looking at Titus 2: 11-13 in relation to Romans 6.

Titus 2
11 For the grace of God has appeared that offers salvation to all people.
12 It teaches us to say “No” to ungodliness and worldly passions, and to live self-controlled, upright and godly lives in this present age,13 while we wait for the blessed hope—the appearing of the glory of our great God and Savior, Jesus Christ