The pump comprises at least one pump element which has a pump piston that is at least indirectly driven in a stroke movement by a drive shaft. A plunger having a plunger body is arranged between the drive shaft and the pump piston and is movably guided in a receiving device in the direction of the stroke movement of the pump piston and is supported on the drive shaft by means of a support element. Lubricant is supplied to the receiving device via a supply line and lubricant is conducted out of the receiving device via a discharge line into the plunger body to the support element. An annular gap filter is provided between the plunger body and the receiving device and is arranged between the supply line for supplying lubricant to the receiving device and the discharge line for discharging lubricant into the plunger body.