Expansion tank empties when car no in use

Does radiator have seperate cap? If so return valve may be stuck

A little difference between the upper and lower level of the expansion tank is usual, depending on the engine coolant temperature. When engine is started, coolant heats up and pressure builds up in the cooling system. The radiator pressure cap would control the pressure and if it is bad, it could result in too much pressure building up or no pressure causing coolant to be sileed out through it.

However if the difference is too much it could indicate the following,

1. A bad head gasket. Radiator require replacement means the engine could have overheated previously and damaged the head gasket. Get a test done to verify this.

2. Air trapped in system. After replacement of the radiator, air would be present but most systems are self bleeding, only thing you need to do is to run the engine for a few minutes, stop engine and wait for it to cool and top up coolant as necessary.
Our database does not have any information of your vehicle so I do not know if there are any bleeder points on your vehicle. Those that do, requires these points to be loosened while topping up the coolant to remove trapped air. These bleeder points comes in different designs such as hex head bolts, nipple, valve with caps (similar to tire valve caps) and some with alan key heads.

Since vehicle had been running and stopped various times, the system would most probably had self bled. Do you still need to top up coolant?

3. Coolant mixture inappropriate. If there are too much water content in coolant, the expansion rate would be more than normal.

4. Bad thermostat. A stuck thermostat would cause overheating and expansion of the coolant.

Try this to see if it helps.

Remove radiator cap.
Check coolant level, top up if necessary.
Turn on heater.
Start and run engine.
If coolant level drops, top up.
Note if there are bubbling of the coolant( bad news if there are).
Do not run engine for more than 5 minutes as the coolant would heat up too much.
Stop engine.
Check coolant level and close radiator cap.
Run engine and retest.