As a high-level overview, you'll need:
A way to sense the current gear that the car is in. This could easily be done by reading which of the 4 LEDs (or what combination of them) is lit.
A way to control the LEDs and 7segment. The easiest way, for me at least, would be to build in a small Arduino or micro controller. Lighting/reading one, two, three, or all 4 LEDs, along with displaying a number on the display, can easily be done with an Arduino and a BCD decoder (for the display). The nice part about Arduino is that it can handle 12V on the Vin pin, which simplifies setup. You'll need at least 7-8 digital pins; four for the LEDs as inputs and at minimum three for the BCD decoder (the most significant bit of the BCD code can be tied to 0 if you are only displaying 0-7, but four would be standard).
And, of course, you'll need to tie it all together and hide it nicely in the dash. Overall, I think this is a pretty neat project idea.