No, there is no single global trademark that provides automatic protection worldwide. Trademark rights are granted on a country-by-country basis, and you need to apply for trademark registration in each individual country where you seek protection.
While there are international treaties and systems that facilitate the filing and management of trademark applications in multiple countries, such as the Madrid System administered by the World Intellectual Property Organization (WIPO), these systems do not provide a single worldwide trademark. They simplify the process by allowing applicants to file an international application based on a single primary application or registration in their home country and designate multiple member countries for protection. However, each designated country's trademark office still independently examines and approves the application.