There are a few options:

You could contact a leather repair service who will come out, prepare a custom colored patch which gets smeared over the area and then dries; you are relying on the person to be good at mixing pigments to get a good color match and sometimes it can stand out as a spot repair.

OR, You could find a faux leather that matches and recover the entire area and if it blends well enough with the rest of the leather, no one will be able to tell the difference. (All of this with the expert assistance of a professional upholsterer, of course!)

OR, If the back of the piece sits up against the wall, remove the leather from the outside back, transfer it to the damaged area, and use a reasonably close substitute faux leather to cover up the outside back; now all of the exposed surfaces are the same. (Again, check with an upholsterer.)

On a related note, oftentimes the seat cushions are the first place to show wear and tear.  A recent trend of mixing multiple fabrics on a piece of furniture gives you the perfect setup to get more life out of  your sofa or chair simply by recovering the seat cushions in any compatible  fabric that speaks to the rest of the piece…ie, tapestry cushions on a leather sofa, or ticking stripes mixed with canvas or duck, or chenilles mixed with damasks – there are endless possibilities. You can even slipcover the original cushions and have a piece do double duty with two different looks.