Trainee drivers can't report directly to the insurance company, because you sign a training contract with the driving school, not directly with the insurance company. The responsibility of the accident vehicle is first borne by the driving school. As for whether it can be compensated, it depends on whether the driving school has insured the accident vehicle, and the driving school will negotiate with the insurance company.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.