There is no such thing as a variable displacement gear pump. It is impossible to change the geometry of the gears or that of their centerline relationship to the gear housing, therefore it is impossible to vary a gear pump's displacement.
However, some gear pump assemblies are manufactured with "load sensing" capability. This seems to imply variable displacement, but in reality it does not. A "load sensing" gear pump has incorported into it's outlet side (or attached to its outlet side) a "load sensing" flow control valve (similar to the LS flow dividers used for steering circuits). The load sense signal controls the spool of this flow control valve and the spool, in turn, diverts flow exiting the gear pump so that the actuator attached to the load receives the flow rate called for by the control orifice.
Bill O'Donnell