Achieving carbon neutrality in industrial ports demands a radical transformation of current energy systems. This paper presents a model-based optimization approach for the operation of a multi-energy cluster, considering a hypothetical evolution of a multi-energy industrial cluster in the Netherlands. The aim is to establish a new system operation strategy that supports the transition towards a carbon-neutral energy system. The synthetic model of the used multi-energy cluster integrates five energy carriers - electricity, natural gas, hydrogen, ammonia, and heat - using an energy hub approach to enable sector coupling and enhance flexibility. Physics-based modeling of electrical power flows is included to ensure technical feasibility in the power system. The model minimizes total cluster's cost while ensuring reliable energy supply. The optimization is implemented in Python by using the PyPSA toolbox and mixed-integer linear programming. A full-year, hourly-resolution simulation under three weather scenarios reveals optimal system operation strategies. Numerical results highlight the benefits of multi-energy cluster operation for managing renewable variability and identify ammonia as a key flexibility provider, supporting hydrogen and electricity systems through conversion and storage. The strategy emphasizes cross-sector economic optimization, dynamic dispatch, and enhanced flexibility, offering practical insights for decarbonizing industrial ports and informing future energy investment planning.