To integrate variable renewable energy sources into the energy system and achieve net-zero emissions, the flexible operation of the power system is essential. Options that provide flexibility include electrolysis, demand side management, import and export of electricity, and flexible power plants. However, the interplay of these flexibility options in a renewable energy system with highly interacting energy and end-use sectors (known as sector coupling) is not yet fully understood. The aim of this paper is to improve the understanding of energy flexibility from a system perspective by explaining which flexibility options can provide how much flexibility and when are they operated. The analysis of the hourly results of the sector-coupled, long-term energy system model REMod shows that in times with high renewable electricity production, sector coupling technologies, specifically electrolysis and power-to-heat, dominate the annual flexibility shares. On the other hand, in times with low renewable production and high non-flexible demand, combined and open cycle gas turbines and electricity imports dominate in winter, while discharging electricity storage technologies dominate in summer. The operation of short-term electricity storage aligns in particular with photovoltaic production, while the operation of electrolysis is especially aligned to wind production. Non-flexible demand variations are driving the operation of combined and open cycle gas turbines and electricity imports. The results emphasize the pivotal role of flexibility, highlighting the need for efficient surplus electricity utilization and sector coupling. The results further suggest that it is crucial to establish market conditions that facilitate the flexible operation of various technologies in order to achieve economic efficiency.