As a minimum, any stylists will require public liability when working on set. We would also usually suggest professional indemnity too. Stylists can and have been caught in legal battles, if they have styled a set incorrectly, or used a prop without clearance on its usage. There was a very serious example of a USA brand pointing the finger at a stylist for not checking what was in the background of the set.
You may also want to insure your equipment, such as laptops and tablets (or cameras if you have those too?). And if you have you own props, and wardrobe, we can also insure that those. And finally, hired in props, they can also be added to your package.
Who would have thought there is so much for a stylist to consider!