Will The Additional Insured Endorsement Actually Cover The Claim?

Imagine this scenario. Your company hires a contractor to do some repair or renovation work. The contract requires the contractor to have commercial general liability insurance and make your company an additional insured under that policy. The contractor does so. Someone is injured on the jobsite and sues your company. You tender the case to the contractor’s insurer. Will that insurer defend and, if necessary, settle the case for your company?