offender
A person who breaks an important rule or law.
An offender is someone who breaks a rule or law. When a student violates school rules by running in the hallway after repeated warnings, teachers might call them a repeat offender. When someone commits a crime, courts and police refer to them as an offender.
An offender has offended against the rules of a game, a school, or society's laws.
You'll often hear the word with a descriptor that tells you what kind of rule was broken. A traffic offender violated driving laws. A first-time offender broke a law for the first time, while a repeat offender keeps breaking rules despite warnings or punishments. In sports, an offender might be a player who committed a foul or penalty.
The word is serious and formal. You wouldn't call someone who forgot to return a library book on time an offender, but you would use it for someone who deliberately shoplifted from a store or repeatedly bullied other students despite consequences. The term recognizes that someone crossed a meaningful line and faces consequences.