Public Engagement in Data Research Initiative (PEDRI) is a sector-wide partnership that brings together organisations working with data and statistics to generate insights that can inform policy and practice. The initiative aims to foster collaboration to advance good public involvement and engagement (PIE) practices within data research, to bring the views of the public to policymakers and data holders in a meaningful way. A roundtable meeting was organised to explore the challenges and potential solutions related to Public Involvement and Engagement in Trusted Research Environments (TREs) and Secure Data Environments (SDEs) at the project level.