The pump may be a closed loop or open loop hyd system, using a charge pump.
Excerpt:
Charge flow is required on all Series 90 pumps applied in closed circuit installations. The charge pump provides flow to make up internal leakage, maintain a positive pressure in the main circuit, provide flow for cooling and filtration, replace any leakage losses from external valving or auxiliary systems, and to provide flow and pressure for the control system.
The pump on the back of the VSP could also be a gear pump for things like boom swing, and other hyd operation.
The pump on the rear of my VSP is a PTO pump for my steering and loader.
You really need a VSP for smooth machine operation.
If you or someone can't fix the VSP you have, then there are replacement from places like Eaton, Danfoss, etc.
You could use all gear pump, but you would have jerky starts and stops with poor control of speed.
The VSP on my machine is used to power all four hyd motors in a closed loop operation where the out put of the hyd motors is fed back to the input of the pump, with the charge pump making up for any leakage from the hyd motors.
Depending on the shaft type, round, splines, hex, etc, one could replace with another VSP using similar dis placement