Have your sister register the car (your name stays on the title and loan documents) and buy her own insurance. That’s the simplest way to handle it, and it happens all the time.
If you’re concerned that she won’t do that properly or you want to be extra-sure that you’re covered as much as you need to be, then you register the car in her name and buy the insurance yourself. You’ll need to be clear to the insurer (the only ones likely to have any legitimate concerns) about who will be the primary driver, where the car will be parked or garaged each night, and the expected daily use.
The lender shouldn’t have a thing to say about who gets to use the car, but the insurer might, if your sister has a bad record, is underage, lives in a high-crime area, etc. But someone will insure the car. Just be sure not to lie on the application, because if you try to ‘shade’ something and a loss occurs, that ‘shading’ could nullify the coverage.
Not a big deal at all.
PS: Welcome to Fluther.
PPS: No one outside of Massachusetts calls it the “Registry” of Motor Vehicles. (At least I’m pretty sure about that. After I left Massachusetts myself, where I grew up, and talked about “the Registry” from time to time and got blank looks, I realized that everywhere else in the country it’s DMV for “Department”.) Just FYI.