change potentiometer threshold

I have a potentiometer that starts at 6k ohms then sweeps up to 10k ohms, I am needing it to control a motorized actuator that uses a 0 ohm to 10k ohm potentiometer, the actuator uses a comparator circuit where the actuator position is controlled relative to the position of the potentiometer, I cannot just replace the 6-10k ohm potentiometer because it is a special style, almost like a tube, and is attached to a board with components in the center of it, is there a device available or circuit that could be built to accommodate this? if not a solution for that, is there a circuit or device available that would allow me to control a servo position with a 6-10k ohm potentiometer that I could then physically mount the 0-10k ohm potentiometer to the servo so the servo would spin it? any input is much appreciated thanks!

 

so basically a circuit that when 6k ohms is appliedto the input, the output would read 0 ohms, then all the way to an input of 10k ohms were the output would be 10k ohms.

 

thanks for the fast input guys, I have determined that the potentiometer in question was bad, I was able to find another board with the same style to compare the values of the 2 and the second one appears to be a normal 10k pot on the meter, here it is for fun, center 3 pins are the pot, outer 2 are for an led located on the outside ring to light up a marker on the knob that snaps over the ring. it just says ALPS 614A... thanks again!

 

They were pots, this is what it’s used for, installing the interior from a 2018 Chevy Silverado into a 1995 Silverado, the 2018 hoax controls are all data driven and require a separate hvac control module all of which I could not find a way to even power up, so I went analog with everything, the fan speed pot wired to the input of a pwm motor controller and temp pot went to the mode door actuator input that required 0-12v to change position of the actuator, turned out great!