Since you didn't specify where your leak is occurring on your water pump, if it's leaking from the gasket area at the rear, or the thermostat area, the gasket probably wasn't coated with water-based lubricant during installation. If this step is skipped on either gasket, if the gasket were nicked or misaligned during in the install, it will result in a water leak.

If the water leak is from the shaft, then the pump is defective. Is it OEM?

If your leak is from the hose area, then there are several reasons for this, but basically due to a bad seal, have the hose and the mating metal spout checked . . . . .