One of the basic principles of business insurance, along with other types, is that you must have an insurable interest in the item, building, asset etc that is to be insured.
For example, you could not take out a commercial building insurance policy on the local supermarket and receive a payout if it suffered a fire. There are two reasons, firstly you have nothing to lose if the building is damaged, and therefore no financial relationship to it and secondly, there will be dual cover in force.
But, there are times when you can arrange a policy for a building that you do not own. This is when the landlord allows you to insure the property, but they have their financial interest, as the beneficial owner, noted on the policy. This is usually through you having a full insuring and repairing lease.
You have, through the signing of the lease, agree to arrange suitable cover. But, if the building were destroyed, then as you are not the beneficial owner, then you do not receive any financial gain.
A full insuring and repairing lease is more rare, but it is always worth checking whether you need to arrange cover.