Procedural justice is essential in climate negotiation spaces to ensure inclusivity and transparency in a global challenge. However, annual Conference of the Parties (COP) meetings of the United Nations Framework Convention on Climate Change (UNFCCC) are increasing in size and complexity, which makes discourse and organisational relationships more uneven and harder to understand. Here, we analyse UNFCCC COP side events during 2003-2023 using topic modelling to understand the evolution of discourse and topic framing. We use participant nomination data to investigate how incumbent business interest groups access COPs and evaluate the relationships between side event organisers and speakers. Among energy side events, we identified growing interests in fossil fuels, marked by a uniquely collaborative organisation network of mainly NGOs. Incumbent corporations gain access to COPs through NGOs in developed countries and through governments in developing countries, with limited presence leading UNFCCC side events. We show the importance of systematically tracing and considering processes at COP as a first step to improving procedural justice at the highest level of global climate governance.