Yes. Your Home Insurance premium includes an amount for natural disaster insurance, which is provided by the Earthquake Commission and is called EQCover.
EQCover provides a maximum cover of $172,500 (incl GST) for residential buildings. If a natural disaster damages your home, the EQC will pay up to this amount to repair or rebuild your home.
Your Home or Landlord Insurance Policy will then top this amount up, to a maximum of your Sum Insured, if it will cost more than this to reinstate your home. EQCover also provides cover for your land within certain limits and conditions.