The steps that need to be taken when an aircraft is involved accident can be tedious. A claim with your insurer and the authorities will result in paperwork, lots of communication and information to be exchanged. But for a quick settlement it is imperative that you do and air law requires you to do so.
The most important thing that needs to be done at the accident scene is taking care of any victims and to protect the aircraft from further damage and making sure it does not become a hazard to anyone in the area. Then contact the aviation authorities, local police and your insurance agent.
You may move the aircraft if necessary (but do take enough pictures before you do) and have the accident scene guarded. Avionics are easily stolen from crashed aircraft.
Whatever happens, refrain from admitting any fault. Discuss the accident only with your insurance company or government officials (CAA, FAA, police). They will conduct an investigation which will reveal all circumstances leading to the accident. Even information not known to you at the time of the accident.
You will need to provide all related important documents to the insurance company. These are (but not limited to): aircraft and pilot logbooks, medical certificates, weather situation during the time of the accident (METAR and TAFs), all photo's taken and any statement by government officials.
Do keep in touch with your agent during this process, this make sure that there won't be any delays in supplying any important documentation to the insurance company.
Your aircraft needs to be inspected for any (including secondary) damage occurred during the incident and the total cost to have it repaired. Have the inspections done by either the manufacturer or an aircraft maintenance company familiar with the type. Make sure to send the report of the damage investigation to the insurance company.
Will your premium rise after an accident? That depends on the circumstances and the cause of the accident. This will be evaluated per case. There are many factors in this process and your agent will look at all of them to see if the risk will remain acceptable.
For example: if the pilot shows bad judgement and flies into bad weather or runs out of fuel and lands off airport with damage to the aircraft then the insurance company may not want to renew your coverage or only at a higher level, reclaiming the cost of the accident. Keep in mind that if the insurance company did not attach the claim surcharge, premiums may rise just because rates will always change no matter what.
It is quite normal that premiums rise annually due to higher cost of aircraft parts and labour to work on the aircraft.