‘For we, through the Spirit, by faith wait for the hope of righteousness.'
For those who are Christians walk through the Spirit by faith. And they are waiting for the final hope when they will be presented holy, unblameable and unreproveable in His sight (Colossians 1:22). This is the Christian Gospel. The grace of God has provided His Spirit to work in men's heart and lives. So those who are His respond to Him in faith with the result that they await the hope of righteousness. Biblical hope is always certain hope. And the Spirit's work is then the guarantee of the final perfection of His people (Ephesians 4:12-13; 1 Peter 5:10) and it all results from the response of faith. To fall away from this, and to try to attain such righteousness by religious ritual and behaviour is to fall away from grace indeed. It is to reject the Spirit.
‘The hope of righteousness.' Either what we hope for because we have been reckoned as righteous (Galatians 2:20), or the hope that we have of being made truly righteous.