3rd party and passenger liability. (I know of a case where pax liability was used after an instructional prang and the student claimed against the instructor; I certainly won't instruct unless that's in place).
Have a look a visicover's website - you can play around with options on their insurance form and see the price differences. (They were also cheapest when I insured the AA5 that I lease to a flying school anyhow, plus very helpful when I contacted them about some complications with it.)
If it's on condition, and through an RTO/ATO, it makes no difference whether the instructor is paid or not - although in my experience, most instructors prefer it
G