It might depend on what your new company is referring to as an "accident" and what you consider to be an accident. For example, your insurance company might not consider not at-fault accidents when they created this discount. If your insurance company has already pulled your CLUE report
(Comprehensive loss report), they've already determined you qualify for their discount based on their underwriting determinations. If they haven't pulled your CLUE report, keep an eye out to see if the discount has consequently been removed.