The use of renewable fuels for internal combustion engines marks a significant stride towards sustainability in transportation and power generation. Ensuring the compatibility of these fuels with existing diesel engines and infrastructure is paramount for a smooth transition. Diesel engines capable of harnessing the advantages of alternative fuels without extensive modifications offer a pragmatic approach to sustainable power for vehicles and industries. This article investigates the impact of carbon-neutral renewable fuel types (hydrogenated vegetable oils, or HVOs, and biodiesel) on the operation of a high-pressure injection pump, focusing on rotational speed and delivery pressure as key parameters. Our investigation, based on pump operating cycle analysis and volumetric efficiency measurements, aimed to investigate to what extent shaft speed and fuel type influence pump performance. Hydrogenated carbon-neutral fluids (HVOs) demonstrate adequate hydraulic capabilities compared to conventional fossil fuels. The findings underscore that while the fluids under consideration vary in viscosity and compressibility modulus, it is the compressibility modulus that predominantly affects the pump’s operation cycle. Diesel (fossil) fluid exhibits intermediate characteristics compared to hydrogenated fossil diesel fluids and biodiesel. The differences in terms of volumetric efficiency are finally reported, showing that hydrogenated carbon-neutral fluids do not significantly hinder the pump’s flow rate transfer capability.