Righteousness is not our future hope, but our current reality by faith.
Paul the apostle was still looking forward to being righteous in the future.
Galatians 5:5 “For through the Spirit we eagerly await by faith the righteousness for which we hope.”
He was still overcoming the righteousness of law and pressing on to the righteousness of faith – having not attained it yet in his life.
Philippians 3 “9 and be found in him, not having a righteousness of my own that comes from the law, but that which is through faith in Christ—the righteousness that comes from God on the basis of faith. 10 I want to know Christ—yes, to know the power of his resurrection and participation in his sufferings, becoming like him in his death, 11 and so, somehow, attaining to the resurrection from the dead. 12 Not that I have already obtained all this, or have already arrived at my goal, but I press on to take hold of that for which Christ Jesus took hold of me. 13 Brothers and sisters, I do not consider myself yet to have taken hold of it. But one thing I do: Forgetting what is behind and straining toward what is ahead, 14 I press on toward the goal to win the prize for which God has called me heavenward in Christ Jesus.”
This is because the law was not yet disappeared in his lifetime.
The law was obsolete on the cross but it was going to disappear in AD70.
Hebrews 8:13 “By calling this covenant “new,” he has made the first one obsolete; and what is obsolete and outdated will soon disappear.”
The law was fully removed in AD70 when Israel was judged.Now we receive the righteousness by faith instantly the second we believe in Jesus Christ because the law passed away.
Romans 4:4-5 “4 Now to the one who works, wages are not credited as a gift but as an obligation. 5 However, to the one who does not work but trusts God who justifies the ungodly, their faith is credited as righteousness.’
For the last 1900 years, believers are not hoping for righteousness but have it as a present possession by faith in Christ apart from any works.