The fan on an outdoor carrier unit won't turn off.
Turned off at thermostate, tried everything, had to turn it off at the breaker.

I am thinking maybe a relay is stuck. Is this a part I can pick up and replace myself or is it a different problem all together

Thanks

Sounds like a thermostat wire issue. If using a round mercury style thermostat and subbase with the heat off cool switches and some other type of equipment that turns the air handler fan on like a woodburner or something of that nature it will back feed through the g terminal to the y terminal on the thermostat subbase in turn kicking on central air unit. Easy fix would be to replace thermostat with electronic type. Most have separate relays to keep from back feeding. Recommend Honeywell pro5000 or pro6000.
Have fun!

The fan on most heat pumps are controlled by a printed circiut board, if just the fan and not the compressor is running the board is probably the problem. If both are running it is a contactor.