Non-compete agreements—contracts that restrict an employee from working for a competitor or starting a competing business after leaving their job—have long been a staple of employment law. For decades, employers used them to protect trade secrets, customer relationships, and investments in employee training. But in New York, and across the country, the legal landscape around employment non-competes is changing fast.

For years, non-compete agreements have been a go-to tool for businesses trying to protect their competitive edge. Employers use them to...