A multiple evidence approach, that brings together Indigenous, local and scientific knowledge systems, is gaining acceptance as key to developing policy-relevant findings to address biodiversity loss globally. The international community is now embracing movement towards to a multiple-evidence approach for climate change research and policy. Parties to the United Nations Framework Convention on Climate Change (UNFCCC) in Bonn in 2017 officially established the “Local Communities and Indigenous Peoples (LCIP) Platform” with the purpose of exchanging experience, sharing knowledge, and accelerating the inclusion of these groups of people. However, the interface with climate science is currently characterised by significant power asymmetries; a recent review identified that 87% of climate studies practice an extractive model in which outside researchers use Indigenous knowledge systems with minimal participation or benefit-sharing with Indigenous communities. Here I present evidence-based practices for working equitably and effectively across knowledge systems, grouped into four categories: respecting rights; supporting care and mutuality; strengthening LCIPs and their knowledge systems; and supporting knowledge exchange. I conclude with a discussion of the potential benefits in terms of legitimacy and salience for climate change policy globally, and some exciting opportunities for engagement across scientific and Indigenous knowledge systems in Australia.