Depends which insurance you are talking about...
For the owner of the aircraft, his third-party and aircraft insurance may require some minimum total hours and hours on type for all pilots operating... but that is his problem to address, not yours..
As far as your coverage goes, as a freelancer, you are totally on your own: I maintain a worldwide accident and health insurance, including additional repatriation coverage.
Additionally, I have a travel insurance covering loss of luggage and such. I have found that the insurances via your gold or platinum credit card will not be sufficient, as I rarely accept to book and pay my own tickets.
Same goes for hotels: as I rarely book and pay for my own hotels, I have an additional private liability insurance which covers me for certain third party damages.
Then there are some no-nos: I never drive a rental car unless I have booked it myself and covered all instances. Also, when ask to transport valuables, or operate expensive vehicles for customers, I have to customer rep releasing me from liability in writing.
When booking expensive services for a passengers, I try to get a release from the rep, and if not possible charge to the airplane without my name appearing anywhere.