An increased penetration of renewable energy sources is essential for the energy transition. A major role will be played by wind and solar, as they are widely available. Hydropower is another crucial resource, currently covering large shares of power generation (e.g., Norway, Italy, Brazil). Despite little expected growth, in a context of increasing electrification, improved integration of hydropower can play a critical role thanks to programmable operation. This work addresses the modelling of hydropower flexibility in energy system models and analyses the impact of hydropower operation on CO2 emission-constrained scenarios. To implement the study, a detailed dataset of the Italian programmable hydroelectric plants is created, using open-source information, covering location, rated power, and storage capacity. Inflow timeseries are derived from historical operational data. These new sets of data are employed in OMNI-ES (a multi-node, multi-sector, and multi-vector energy system model) to study optimal configurations and operation of the Italian energy system in decarbonisation scenarios, such as net-zero-CO2 and Fit-for-55 targets. Considering different operational strategies and multiple historical reference years (impacting the inflow), results demonstrate significant changes in hydropower behaviour and highlight its relevance as zero-carbon resource in terms of both power and energy output, influencing the installation of other technologies.