Short answer: Being legally allowed to supervise is not the same as being insured to drive the vehicle. Check the learner’s cover, the car owner’s policy and any cover the supervisor expects to rely on before practice begins.
Separate three questions
First check whether the supervisor meets the legal age and licence-history rules. Then check whether the learner is insured to drive the particular car. Finally, check whether the supervisor is insured if they need to take over. A policy can impose conditions that are stricter than the legal minimum.
What to check in the documents
Look for the definition of an eligible supervising driver, any minimum age or licence-tenure rule, the permitted licence jurisdiction and whether the supervisor must be named on a policy. Do not assume “driving other cars” cover applies: it is policy-specific and often restricted.
Before each practice session
Confirm that the learner’s cover is active for the correct vehicle and dates, the car remains otherwise insured where required, the supervisor still meets the stated conditions and both drivers know who can drive the car home.