You can sometimes find replacement shingles, but I have not seen successful repairs of chips and cracks. Given the hazards of this siding, I prefer to cover it over or have it removed. I have covered asbestos cement siding with vinyl with good results. Today, I would be inclined to remove the siding to preserve my home value. Asbestos is a significant value detractor due to the panic that surrounds the "A" word. This can be done as a DIY project saving many thousands of dollars. You just have to take reasonable minimal precautions.
If you are going to remove or make cuts in the asbetos siding, I recommend you obtain an appropriate respirator and have it properly fit-tested. For a modest fee, you could consult with a safety expert or industrial hygienest that could set you up to safely work with the material.