Since 2016, a group of senior women organized in the association KlimaSeniorinnen Schweiz have been trying to legally force the Swiss government to take stronger climate protection measures. Parallel to the pursuit of a climate lawsuit, the KlimaSeniorinnen have developed into a growing social movement that is present in the media and participates in the public debate on climate change. Building on this specific climate litigation case, the present article analyzes the strategy formation of new actors in the field of climate governance. Based on existing concepts of social movement research, the strategy formation of the KlimaSeniorinnen is reconstructed in terms of a strategic actor who pursues certain strategic orientations in given strategic contexts. The empirical analysis of the strategic context (by means of opportunity structures), the strategic orientations (via collective action frames), and the strategic actor (by means of interviews) shows a double strategy. On the one hand, the KlimaSeniorinnen attempt to address a specific legal opportunity structure with an ‘injustice frame,’ which emphasizes human rights and the special vulnerability of older women to intense heat waves. On the other hand, they want to mobilize public support for an ambitious climate policy by additionally promoting a ‘grandchildren frame,’ which articulates altruistic values, such as responsibility towards future generations. Based on this analysis, both practical implications and consequences for future research on a new climate politics, which is increasingly taking shape between and across different arenas, are discussed.