Salvation is spoken of in 3 distinct tenses.
We are saved.
We are being saved.
We will be saved.
All three are true. We have been saved, but we are not yet fully saved. If there is no future resurrection, then we are without hope in this world. We have not yet attained the goal, the prize, we are currently in the process of being saved (sanctification). One day, we will be fully saved, in fullest meaning of the term.
Same with the heart. If we are born again:
We have a new heart.
Our heart is being transformed by God.
One day we will have a perfectly clean, without a trace of sin in it, heart.
We haven't obtained that last one yet.
Here is some good stuff from John Owen and someone else summarizing him:
The Nature of the Human Heart according to Scripture
Owen refers to the “heart” numerous times and in this section takes a moment to describe what he means by the term. Generally speaking, “heart” in Scripture refers to the whole of a man considered in his desires, decisions, and plans; it refers to man viewed as a morally responsible being. Owen comments:
The
heart in the Scripture is variously used; sometimes for the
mind and understanding, sometimes for the
will, sometimes for the
affections, sometimes for the
conscience, sometimes for the
whole soul. Generally, it denotes the
whole soul of man and all the faculties of it, not absolutely, but as they are all one principle of moral operations, as they all concur in our doing good or evil.
22
....
The Heart Is Unsearchable
The heart is virtually unsearchable to human beings. Certainly no one can fully understand the heart of another person and no person can fully understand his/her own heart either. The human heart is fully pervious to God alone; only he can plumb the depths of our hearts and render an accurate verdict as to what he finds there. And, remember, it is in that
unsearchable heart that the law of sin dwells.
Much of the strength of indwelling sin, then, lies in this fact, namely, that the heart itself is beyond understanding. This allows sin to have its sway and power. Thus we may suppose a certain sin to have been defeated when in reality it has only temporarily slipped out of sight-where we cannot follow it and destroy it—only to reappear at a more convenient time.
3. The Seat of Sin, the Heart | Bible.org
Blessings,
Travis
p.s. one more:
Mortification Never Ends in This Life
The redeemed soul, by the grace of God and his indwelling Spirit (Rom 8:13), must press on toward perfection. To this it has been called. Thus, our role is one of co-operation with God, in which we put to death the misdeeds of the body (Phil 2:12-13). And we shall do this for as long as we are in this body. Only at glorification, in the next life, will there be no need for mortification. How much more do we realize this now, since we have come to understand that the very home of sin, i.e., our hearts, is deceitful? The person who dies fighting this fight, dies a victor. As Owen says,