Purchase a condensate pump from your local hardware store, furnace supply, Bryant dealer or home improvement center. Generally, at the time of publication these retail for around $40 to $70 depending on your location and the power handling of the unit. Make sure that the pump you purchase is capable of handling the output from the furnace or you’ll risk burning up the pump.
Turn off the power leading to the heater and open the main unit panel on the front side of the furnace by gently pulling it up and out. It should pop off without much hassle. Underneath, toward the floor, you’ll see the air blower and next to it the condensate pump, which is about the size of a toaster. The pump is the actual mechanism that redirects condensation and it rests on the basin, which is a reservoir that takes water not channeled down a nearby drain.
Unscrew the four holding screws that anchor the unit to the frame. Pull off the pump assembly first, then the basin unit by unscrewing the holding screw in the bottom. Note that there may be some water run-off. If so, dump the water. Once you have removed the old pump, slide the new pump assembly in place and refit all the screws. Secure the pump to the top of the basin if necessary (some replacement units may come preassembled).
Run the line drain hose to a nearby laundry sink, sump pump pit or basement drain hole. Your old unit may not have had a drain hose, thus the reason for the water buildup that's causing the leaking water. If your Bryant unit is situated too far from a suitable drainage point, run the flexible line into a large plastic bucket, although you’ll have to keep an eye on it and empty it so it won’t overflow.