A pressure supply device is provided for a hydraulic braking system of a vehicle including a first pressure chamber and a second pressure chamber, which are delimited by at least one piston of the pressure supply device, a motor and a gear unit, with the aid of which the at least one piston is displaceable at least in a first direction with the aid of an operation of the motor, an exceeding of a predefined maximum pressure difference between a chamber pressure present in the first pressure chamber and a reservoir pressure present in the brake fluid reservoir being preventable with the aid of a reservoir isolating valve, which is connectable to a brake fluid reservoir of the braking system, hydraulically connected to the first pressure chamber via an opening of the reservoir isolating valve. Also described here is a hydraulic braking system for a vehicle. In addition, a method is provided for operating a hydraulic braking system of a vehicle.