There's no such thing as a global trademark. Trademark protection extends only to a single country or a multi-country jurisdiction (e.g. the European Union) in some cases. It is possible to register a trademark in every single country and territory in the world; however, that would be too expensive and too hard to manage since that would constitute over 190 separate trademarks.
It is possible to somewhat simplify this process by applying through the World Intellectual Property Organization (WIPO), but this route has its caveats (application has to be based on a previous application filed in one of the member states) and still doesn't give you a global trademark - it just streamlines the application process.
However, there are other steps you can take that provide a high level of legal protection and have a better price-to-result ratio. If you're considering trademarking a (potentially) international brand, you can strategically select countries in which you're currently doing business or where you plan to expand in the near future. You can always add more countries later as your business grows since, as already mentioned, each of these trademarks requires separate filing.
If you already have a list of countries where you'd like to register your trademark, you can consider a global registration provider that can offer multi-country packages and register all your respective country trademarks at once. That way, you don't have to seek legal representation in each of your chosen jurisdictions.
You can learn more about protecting a business in each stage of its growth in our article on optimal trademark strategy. You can also check our international packages, which include country combinations most commonly sought by other business owners.