I have a ac/heat pump. I used the heat pump the other night. The disired temp was reach, but the condenser fan will not shut off unless I turn it off at the breaker. Could this be a relay issue or thermostate issue?

The relay done it. As a check, you could cut off the breaker to the air handler which usually supplies power to the thermostat. Leave the breaker for the condesner on. If the fan keeps going, it is not the thermostat.