Biodiversity loss is one of the most significant drivers of ecosystem change and is projected to continue at a rapid rate. While protected areas, such as national parks, are seen as important refuges for biodiversity, their effectiveness in stemming biodiversity decline has been questioned. Public agencies have a critical role in the governance of many such areas, but there are tensions between the need for these agencies to be more “adaptive” and their current operating environment. Our aim is to analyze how institutions enable or constrain capacity to conserve biodiversity in a globally significant cross-border network of protected areas, the Australian Alps. Using a novel conceptual framework for diagnosing biodiversity institutions, our research examined institutional adaptive capacity and more general capacity for conserving biodiversity. Several intertwined issues limit public agencies’ capacity to fulfill their conservation responsibilities. Narrowly defined accountability measures constrain adaptive capacity and divert attention away from addressing key biodiversity outcomes. Implications for learning were also evident, with protected area agencies demonstrating successful learning for on-ground issues but less success in applying this learning to deeper policy change. Poor capacity to buffer political and community influences in managing significant cross-border drivers of biodiversity decline signals poor fit with the institutional context and has implications for functional fit. While cooperative federalism provides potential benefits for buffering through diversity, it also means protected area agencies have restricted authority to address cross-border threats. Restrictions on staff authority and discretion, as public servants, have further implications for deploying capacity. This analysis, particularly the possibility of fostering “ambidexterity” —creatively responding to political pressures in a way that also achieves a desirable outcome for biodiversity conservation—is one promising way of building capacity to buffer both political influences and ecological pressures. The findings and the supporting analysis provide insight into how institutional capacity to conserve biodiversity can be enhanced in protected areas in Australia and elsewhere, especially those governed by public agencies and/or multiple organizations and across jurisdictions.