Recently, the O-RAN architecture started receiving significant interest from the research community. The open interfaces and especially the possibilities for network-wide control protocols via the Near-Real Time RAN Intelligent Controller provide a significant amount of opportunities to implement newly proposed algorithms from state-of-the-art research. O-RAN follows the trend towards disaggregation of network functionalities which is especially interesting to deploy Cell-Free Massive MIMO in realistic distributed networks. Many attractive solutions have been proposed for the physical layer in Cell-Free Massive MIMO networks. Unfortunately, only limited work has been performed to map these solutions to the Next Generation of Radio Access Networks, especially also considering the existing control plane interfaces and the impact on network-level resource allocation and handover. In this work, we propose a realistic and elegant method of modelling the temporal evolution of the channel in cell-free Massive MIMO. We then build clustering and handover strategies and provide numerical results for multiple deployment scenarios. To realistically evaluate handovers and dynamic clustering for cell-free in O-RAN, we consider a fixed clustering strategy, which computes the ideal cluster whenever a handover threshold is exceeded, and an opportunistic clustering strategy, where serving units are added opportunistically as the user moves. Additionally, we map an uplink detection method from the current cell-free Massive MIMO state-of-the-art to the O-RAN architecture. We study how the ageing of the channel and especially the user-centric cluster around the UE limits the performance of Cell-Free algorithms. We identify what is currently possible and propose the few needed extensions to O-RAN to fully exploit state-of-the-art cell-free processing schemes.