Process mining, a specialised form of data-driven process analytics, is concerned with evidence-based process improvement. Process mining relies on process data, which often suffers from data quality issues that may be hard to detect and rectify. Data governance, recognised as a business capability, was recently introduced to manage data, including its quality, to maximise data's tactical value. Interestingly, no tailored data governance approach for managing process-data quality exists. The paper bridges this gap by introducing a data governance framework, the ImperoPD framework, for process mining with a focus on data quality. We use a capability-based approach and conduct a theoretical review of 75 papers to identify 20 capabilities an organisation should possess to implement process-data governance successfully. The framework is validated for its utility and comprehensiveness by 11 data governance experts. It contributes to an understanding of what is required to implement a data governance program for process mining.