Standard homeowners insurance policies typically do not cover the cost of damage to your home from sinkholes.
Sinkholes by most insurance companies are usually covered under earthquake insurance or other ground movement insurance.
With some insurance companies you'll need to purchase sinkhole insurance as additional coverage on your homeowners insurance policy.
The sinkhole insurance that you add to your current homeowners insurance policy will raise your homeowners insurance monthly cost up at least a bit.
You'll pay additional money for the sinkhole insurance coverage.