Sorry to hear your fence was damaged. The good news is, the repairs to your fence will be covered by your homeowners policy.
Fences are covered by the other structures coverage section of your homeowners policy. This covers all the physical structures on your property other than your house. This includes fences, pools, and sheds.
To be covered, the damage to your fence must be caused by a named peril. These are sudden, unexpected damages that are listed on your lease. The good news is, almost every homeowners policy will cover storm damage. Some other common named perils are fires, theft, and windstorms.