In this paper, we study conveners' work in establishing change towards sustainability through cross‐sector social partnerships (CSSPs). Applying a paradox lens, we offer a new perspective on tensions in CSSPs: These are not hurdles or challenges to overcome in order to reach success but endure throughout the entire CSSP process. This insight changes the role of the convener, who no longer has to overcome but has to navigate tension. We focus on two tensions related to the convener role: the convener as leader but without formal authority over CSSP‐partners and the convener as both stakeholder and (neutral) facilitator in the process. Through a case study on a CSSP in the Dutch timber sector, we explain how a convener (Forest Stewardship Council Netherlands) responded to these tensions over time. We add to literatures on CSSPs and convening by outlining the relevance of a paradox perspective in this domain.