Often yes, and some policies include endorsements that allow you to rent your aircraft to specific pilots. Regardless of the arrangement, tell your broker before you do it. A dry lease to another person or entity under Part 91 is common. The underwriter may need to add the lessee to the policy, sometimes for an added fee. If you’re looking to operate commercially or making a profit you should speak with a knowledgeable aviation attorney. If you’re putting your aircraft on a flight school’s leaseback line, the school’s policy usually covers it. Make sure you get a leaseback owner certificate naming you as additional insured, with a waiver of subrogation, and as loss payee.