I live where there are lots of sinkholes, close to sinkhole alley, but not in it. Sinkhole insurance is purchased separately like earthquake and wind, so you only have it if you bought. You can of course call your insurance and find out what you have.
There are two types of sinkhole insurance. One, covers you if you start to see signs of a sinkhole to repair before something really bad happens. The other, covers you after catastrophic damage happens.
I’m not sure if any insurance will help if the hole isn’t affecting your house yet.
What you have might not technically be a sinkhole. You probably should get the property evaluated and make sure there isn’t other stuff going on under your house. I think there are several ways to do that, but unfortunately I don’t know them all. The only thing I’ve done is evaluate the soil before building or used evaluations done by builders.
It might be the soil was never packed down well in that spot near the surface and not a sinkhole. You never mentioned how deep it is. It might just be a pothole in your driveway.
I’d ask locally for information. My guess is there are companies who gouge, because it’s a scary topic. Shop around.
Don’t be very freaked out. It might not be a sinkhole and even if it is it might be very small. They say when they repair a sinkhole your house becomes the safest one on the block.
Sinkhole would have to be disclosed if you ever sell. Some states probably have more specific questions about it than others on a standard disclosure.