As soon as your auto insurance company learns that you've been convicted of driving while intoxicated, they'll apply a major surcharge to your policy. While this may occur on the first renewal date after your conviction, it's possible that they'll levy the charge retroactively to cover the period during which you "hid" your conviction.
Alternatively, your state may require you to notify your provider immediately after your conviction. In most jurisdictions, you need to obtain an SR-22 form from your insurance company in order to retain your driving privileges once your DUI-related license suspension period ends. It's unlikely that you'll be able to request an SR-22 from your insurer without alerting them of your recent conviction.
Once your DUI is a matter of record, you'll endure years of artificially high premium payments. You won't be able to do much about this: Whereas "safe" drivers can switch insurance companies freely to take advantage of promotions, deals and novel policy features, "high-risk" drivers who wish to switch insurance companies must contend with fees and red tape. Once you have a DUI on your record, it's unlikely that you'll find a better deal with another provider.
In most states, your DUI will remain visible to your insurance company for five years. Unfortunately, this is not the case everywhere. In Massachusetts, your DUI conviction will remain active on your driving record for an entire decade. In Alaska, you'll never escape the stigma of your lapse in judgment.
You can mitigate the financial impact of your DUI in several ways. First, figure out exactly when your DUI conviction will drop off of your driving record. Unless you take out a new insurance policy each month, it's unlikely that this will occur immediately before your policy is up for renewal. To avoid paying hundreds of dollars more than you should, call your insurance company a few days before the five-year anniversary of your conviction and ask your agent to recalculate the cost of your DUI-free policy.
If you sell your car after your conviction, cancel your current policy and obtain "operator-only" insurance. This type of coverage permits you to drive without permanently tying you to an actual vehicle. Alternatively, you can purchase low-cost "proof of insurance" from an online provider. While it may not provide much protection in an accident, this type of coverage is legal and may save you hundreds of dollars per year.