Yes. In many cases, a business can be registered after it has already started operating. The process and legal consequences depend on the type of business, when it began operating, and the laws in your jurisdiction. However, the business owner may still need to address any prior noncompliance, missed filings, taxes, fees, penalties, licensing issues, or other legal obligations that arose before registration.
Registering your business after you have started can help formalize your operations and meet legal or regulatory requirements. However, it may not eliminate obligations that arose before the business was registered.