How does the Gospel fuel our battle with indwelling sin as believers? Tim Chester, in his book You Can Change gets us on the right track for thinking about this. Chester wrote:
You will cleanse no sin from your life that you have not first recognized as being pardoned through the cross. This is because holiness always starts in the heart. The essence of holiness is not new behavior, activity, or disciplines. Holiness is new affections, new desires, new motives that then lead to new behavior. If you don’t see your sin as completely pardoned, then your affections, desires, and motives will be wrong. You will aim to prove yourself. Your focus will be the consequences of your sin rather than hating the sin itself and desiring God in its place.