I'm not sure I fully understand the question, but the basic premise is that you don't want to overpressurise your vessel. This therefore requires you to have adequate pressure relief. You mention that the vessel has a vent, but you don't say whether you have an open vent, or whether it is pressure relief protected. If it is an open vent that is adequately sized for the inflow from the pump, then you don't need a pressure relief device, because, in essence, you have one. You may overfill the vessel, but that is a different issue.
If, on the other hand, what you are trying to do is to stop a relief valve on the vessel at 4 bar from lifting, then I suggest you put a relief valve from the pump discharge going back to somewhere on the suction side of the pump. A pressure regulator on the fluid would do a similar job, but is likely to reduce your flow. A pressure regulator on the air would similarly reduce the flow. On these type of pumps, a low air pressure will cause a substantial flow reduction.