Will my home insurance increase if I file a claim for a natural disaster storm

This question is probably more appropriate for your insurance agent, as each company is different about how they handle damage claims and premium determinations.  But to attempt to answer your question, there is always a risk that your insurance premiums will increase any time that you make a claim under the insurance.  But, again, each company is different, so it is best to speak with your insurance agent about this issue.