Contact your insurance company.
EQC (Earthquake Commission) may also provide some cover. To get EQC cover, you need to have a home or contents fire insurance policy with a private insurance company when the natural disaster damage occurred.
While it may speed up the process if you make a claim quickly, you have three months from the date of the damage to lodge your claim.
See eqc.govt.nz/recent-events or contact them on 0800 DAMAGE (0800 326 243).