The main motivation for the extraordinary advances in the field of predictive process monitoring has been to enable data-driven prediction of potential violations in process performance and the subsequent improvement of processes in organizations through continuous process re-engineering in enterprises. The contribution of predictive process monitoring is instrumental and is a first step stone towards automating process performance improvement. Building on the advances in predictive process monitoring, in this paper we focus on the next steps towards autonomic process performance improvement. The other essential contribution towards this goal is served partly by the research in the field of process adaptation and flexibility. We show that the link and interplay between predictive monitoring and process adaptation, both in terms of underlying concepts and technological realization, have been inadequately researched, as revealed by our review of existing literature, leaving a huge gap towards completely automating the reaction to predictions produced by runtime monitoring techniques, or business experts for that matter. We also define and present a functional architecture that aims at assisting enterprises in developing solutions and the research communities when positioning their research findings in the broader fields of predictive process monitoring, process adaptation and enterprise architectures. Towards that goal, we also contribute a road map highlighting potential pitfalls and pointing to best engineering practices towards the realization of autonomic process performance improvement in enterprise systems.