No, you cannot add accident forgiveness after an accident in order to get that same accident forgiven. Accident forgiveness is designed to be purchased or earned in advance, so it cannot be applied retroactively after an accident.
If you recently had an at-fault accident and want to buy accident forgiveness for future crashes, some insurers will allow you to purchase an accident-forgiveness add-on. For example, Allstate offers Gold and Platinum auto insurance packages, which are available at an additional cost and provide accident forgiveness with no eligibility requirements. On the other hand, accident forgiveness from insurers like Progressive and State Farm requires years of a clean driving record, meaning you cannot get it soon after an accident.
If you don't have accident forgiveness already, you will likely be stuck paying increased premiums after an at-fault accident. However, having an at-fault accident is a good time to compare quotes, since every insurer will raise your premium by a different amount after an accident. And keep in mind that for small amounts of damage, it might be cheaper to pay for repairs yourself than to file a claim and increase your insurance costs in the long-run.
Accident forgiveness eligibility varies by state and insurer, so call your agent or insurance company if you're wondering whether you qualify. And if you are paying higher rates due to an at-fault accident, check out WalletHub's guides to Switching Car Insurance Companies and Car Insurance Discounts.