resistor
it seems your title is rather mis leading, you have stated that you do not know what the part is
The part is mini Potentiometer.
I suggest:
If you cannot find a exact replacement, you will have buy a standard Potentiometer and make some modifications.
look on the internet and look for linear Potentiometer, with a built in shaft rated at 10k ohms. If you cannot extract the knob of the old one and transfer it, you will have to buy a matching knob.
Solder the pot, and make sure you mount it the correct way, maximum resistance when fully wound clock/anti clockwise.
Hope this helps