Under contract you may be required to provide insurance which is primary and non-contributory.
In insurance terms, the right to contribution arises when several insurers are obligated to indemnify the same loss, with one insurer paying out more than their proportion of the loss and looking for reimbursement of that paid cost, from any other insurance policy available.
Providing insurance which is primary and non-contributory notes a contractor under your insurance as an additional insured, with the agreement that your insurance policy will be the primary, or the first response in the event of a claim and that your insurer has given up their right to any proportion of contribution from any other insurance policy available to the additional insured.
Needless to say, this has to be specifically agreed with your insurer prior to acceptance of any contract.