Indigenous peoples and local communities live in, manage and own vast areas often rich in biodiversity and critical for ecosystem services. Bridging indigenous and local knowledge systems with scientific knowledge systems is vital to enhance knowledge, practice, and ethics to move towards sustainability at multiple scales. We focus on international science-policy processes and present a framework for evidence-based guidance on how tasks to mobilise, translate, negotiate, synthesise and apply multiple forms of evidence can bridge knowledge systems. Effective engagement of actors, institutions and knowledge-sharing processes is crucial in each of these tasks. We use examples from the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) and the Convention on Biological Diversity (CBD) to illustrate and discuss our framework.