Indigenous research leadership can enhance research benefits to Indigenous communities. Our research investigates how Aboriginal and Torres Strait Islander (henceforth Indigenous) leadership is expressed in the context of academic research, and how Indigenous leadership is supported or constrained in such context. This exploratory study includes semi-structured interviews with 20 Indigenous Australian researchers and document analysis. The thematic content analysis suggests that 'Indigenous leadership in research' refers to features, qualities or processes that enable certain outcomes, rather than formal ranking. Our research proposes a model connecting Indigenous leadership features in research with the achievement of (social) research impacts. The performance measures valued in academic research reflect a limited part of leadership as expressed by interviewees, hindering the achievement of higher hierarchical positions by those who holistically pursue such a leadership model. We suggest changes in the incentive structure and performance measures to better support Indigenous leadership in research.