No, you can’t print in leather — at least not yet. But [Make Everything] has a tutorial about how to produce a custom leather embossing jig with a 3D printer. From a 3D printing point of view, this isn’t very hard to do and you might want to skip over the first six minutes of the video if you’ve done 3D printing before.
The real action is when he has the 3D print completed. He glues the stamp down to some wood and then fits the assembly to a vise that he’ll use as a press. After wetting the leather, the wood and 3D printed assembly sandwiches the piece and the vise applies pressure for ten minutes. He did make the leather a bit oversized to make alignment more forgiving. After the embossing is complete, he trims it out.
If you are experienced with leather, this probably isn’t a revelation. But if you are not wise in the ways of tanned animal hide, this is an easy way to add a capability to your workshop using nothing more than what you already probably have. All you need is some leather.
If you decide you want to go all out working with textiles, we can help you. We’ve actually seen 3D-printing done for leather book covers before, although the technique is quite a bit different as the plastic stays in and the text is outset.