Having it and putting it on are two different things.

You were taught, with regard to your former way of life, to put off your old self, which is being corrupted by its deceitful desires;
23to be made new in the attitude of your minds; and to put on the new self, created to be like God in true righteousness and holiness. (Ephesians 5: 23-24)

For most of us after going through a process of tossing here and there on the matter of faith, we come to a conclusion that by believing and receiving Christ and Christ alone God gives us the authority to become His children. That is where spiritual life starts. It also means that we are a new creation, a new self. I think having a new self and putting it on are two different things. Having a new self is a gift from God and there is absolutely nothing we do to attain it. But putting the new self on is a continuous attitude of our heart. (Again, it is an attitude of heart, it is not a work.)

It is up to us to 'put on' the new self and 'put off' the old self. The fact is that the old self is gone for ever but we can still act as the old 'caterpillars' though we are butterflies. Here in Ephesians, Apostle Paul is encouraging us to 'put off' our old self, our former way of life, life of hopelessness, life as the children of darkness. He says, 'to be made new in the attitude of our minds' and to 'put on the new self' which is created to be like God in true righteousness and holiness. Our new self is created to be like God! The imparted righteousness is no less that His own righteousness. It is amazing!

We enter God's tapestry, we are His children who are truly righteous and holy. There is nothing we can do to add or subtract from it. It is a done deal. But we still have the potential to act as the 'old person'. It is the attitude we develop over the time by the renewing of our mind, enabling us to set our heart on the things above. Romans 12:2 reminds us about the continuous transformation by renewing of our mind.

NLT says to 'throw off' the old self and 'put on' the new self. NLT also does a good job on verse 23: it says, let the Spirit renew your thoughts and attitudes. So it is the Spirit who does it or we allowing the Spirit to do it, we allow the Word of God to do its work in us on a daily basis.

AMP says, Be constantly renewed in the spirit of your mind [having a fresh mental and spiritual attitude], And put on the new nature (the regenerate self) created in God's image, [Godlike] in true righteousness and holiness.

We have the coat, it is ours but we can still hang it there in the closet or wear it. it is up to us! No matter what we do coat is always ours.

Having a 'fresh mental and spiritual attitude' about who we are in Christ is so refreshing, so uplifting, so relieving, so peaceful, but we keep forgetting it. CS Lewis once said, "people need to be reminded more often than they need to be instructed."