What is the synonym for urging someone to commit an offense?

The term that best fits the definition of urging someone to commit an offense is "instigate." To instigate means to incite or stir up someone to take action, particularly one that involves wrongdoing or an illicit act. This word carries a connotation of provoking or initiating a negative action in another person, making it the most accurate synonym for urging someone to engage in misconduct.

While "encourage," "assist," and "exhort" may imply support or motivation, they do not necessarily have the same implication of instigating wrongdoing. "Encourage" generally refers to promoting or motivating positive behavior, "assist" indicates providing help without the connotation of wrongdoing, and "exhort" means to strongly urge someone to do something. However, exhortation can be positive or negative, but it’s not specifically tied to committing an offense like "instigate" is. Therefore, "instigate" specifically captures the intent of prompting someone to carry out an illegal or immoral act.