Formal:
* Redemption: This implies a chance to atone for past mistakes.
* Rehabilitation: This refers to a chance to improve or restore oneself.
* Reparation: This implies a chance to make amends for wrongdoing.
* Renewal: This suggests a fresh start or a chance to begin again.
* Restitution: This signifies a chance to compensate for losses.
Informal:
* Do-over: This is a casual way of saying someone gets another try.
* Another shot: This means another opportunity.
* Fresh start: This implies a chance to begin anew.
* Second wind: This refers to a renewed burst of energy or motivation.
* New lease on life: This implies a chance for a happier or more fulfilling life.
The best word to use will depend on the specific situation and the tone you want to convey.