A global concern in recent years has been the formal incorporation of computing and digital technology subjects into high school curricula. Despite many initiatives to make these subjects accessible to students, significant barriers to uptake remain in many countries. In this study we convened a panel of 32 academic, research, and other experts from several countries, to participate in a three round Delphi study with the goal of identifying ways to improve student participation for high school computer science and programming subjects in New Zealand. The study explored barriers and challenges, potential solutions and future scenarios, as well as implementation ideas for the most important solutions across five domains: Computer Science and Programming Standards, Resources, Support, Assessment, and Student-centred factors. Together these three Delphi rounds were synthesized into a framework summarizing challenges and potential solutions, including suggestions relating to the implementation of those solutions, alongside key aspects of a likely and a desirable future scenario regarding high school computing in New Zealand. The framework, which is the major result of this study, was designed with the intention to summarise and present potential ways to increase student participation and engagement for computer science and programming standards. We hope that this framework will be of interest to government, teachers, schools, industry, universities and other key stakeholders.