Read up on leather.
For the common stuff, read up on people fixing old leather boots and stuff.
I am sure you could send the whole coat out for a "redye" or however that would get spelled but overall it is one of those things where I would look at it as an old pair of boots that needs some work.
Not sure I would get out the black shoe polish, but after some reading I very well might.
Seen folks at work scuff up their boots on concrete, kneeling down and dragging the toe and what not, and just find a black permanent marker and color it black. Once they get around to messing with the boots properly at home it helps it blend in better.
People can restore ancient leather seats in valuable old cars. You have a leather jacket, a drycleaner more than likely has someone or someplace he can send it out to for repairs and recoloring and what not, but I doubt I would spend the money on it.
Also consider all the people who make leather belts and holsters and stuff, they have to color it and treat it and take care of it as well.
Read up on your options. There are many options. Part of it will depend on how much you want to spend money and/or timewise on it. The other part is what you want as a finished product.
Someone posted some leather care products easier, there are all sorts of things at amazon or anywhere if you go look. At wally world stop in their shoe section and take a gander at the shoe/boot care center. It has everything from shoo goo glue or whatever it is called to shoe polish to water proofer and leather cleaner and other stuff as well I expect.