Yes. Charter yachts are insured by their owner or the charter company. Ask the charter company for proof of insurance if you want to see the cover and the liability limits.
What does the yacht's insurance cover?
It covers damage to the yacht itself, for example after an accident or a storm. It does not replace your own responsibility as the person renting the boat.
Who pays if the yacht is damaged?
If the yacht is damaged during your charter, you, as the renter or skipper, are usually liable up to the amount of your security deposit. That is why the deposit is held.
Read the charter company's terms so you know what you are responsible for and what to do after an accident. Ways to reduce the risk to your deposit: What is a damage waiver? and What additional insurance should I purchase for my boat rental or yacht charter?