Legitimation and Trust Strategies for Sustainability in and for Global Sport Events: The Case of the ‘Climate Positive’ Brisbane 2032 Olympics

International sport governing bodies are increasingly under scrutiny due to their questionable environmental sustainability records of global sport events, thereby facing a potential legitimacy gap and loss of trust that the proclaimed sustainability goals can be achieved. However, despite the critical importance of legitimacy and trust for sustainability in and for sport events management, sport academics have not only stayed relatively silent on this important relationship and the distinction between those two concepts, but also on the strategies that can be implemented to increase legitimacy and trust. As a response, we use the case of the upcoming Brisbane 2032 Olympic Games—the first to be contractually obliged to be delivered as ‘climate positive’—to examine the role of legitimacy and trust for sustainability in global sport events. Based on secondary data, we (a) provide a taxonomy distinguishing legitimacy and trust aspects, (b) present a framework explicating the relationships between legitimacy and trust aspects for the Brisbane 2032 Olympic Games, and (c) suggest concrete strategies to increase legitimacy and trust for the climate positive Brisbane 2032 Olympic Games. These findings will support local authorities, sport event managers, and policymakers in their decision making leading up to the Brisbane 2032 Olympic Games.