The immense pressure to decarbonise the maritime industry has led to the Liquefied Natural Gas (LNG) uptake as a marine fuel and the LNG fuelled ships design. As LNG is stored in cryogenic conditions, the heat ingress from the ambient causes the boil-off gas (BOG) production, which, if not controlled, results in the tank overpressure with implications on the fuel storage system safe operation. This study aims at investigating an LNG storage tank behaviour for realistic operating conditions of an LNG fuelled ocean-going ship, targeting to identify the recommended control actions for avoiding tank overpressure. A dynamic model is developed by considering the mass and energy conservation in the liquid and vapour subsystems, the energy conservation in the tank walls, the vapour to liquid equilibrium (VLE), and real gas properties. Following the model validation for a holding test, simulation runs were performed for various operating conditions corresponding to typical long and short voyages of the investigated ship. The simulation results demonstrate that a boil-off gas (BOG) compressor capacity of 450 kg/h along with its on/off control setting the upper and lower limits of the tank absolute pressure at 5.5 and 4 bar leads to tank overpressure avoidance and the minimum number of BOG compressor activations.