I Have A New Honeywell thermostat that I just installed. And all of the colors are matched up it seems but my air handler will not shut off with my outside unit? And I have replaced the air handler electrical-contactor.

Check the thermostat and make sure the fan switch is on auto, not fan. Check the G terminal at the air handler to make sure it does not have 24 v to the B or C terminal. The air handler also has a timer that should let the blower run 90 seconds after the thermostat shuts the compressor off. It could be sticking.

The contactor was a likely suspect, but not always the problem.