Here, you would be the prime contractor. Your insurance and your workers compensation would take precedence.
The subcontractor should still have their own liability insurance and workers compensation. But if the subcontractor or one of their employees breaks a compensation rule or gets hurt on your job site, it is your compensation insurance and reputation that is effected.
Your liability insurance should cover you and your subcontractor.
Bottom line though, talk to your insurance company and read the documents for the actual answer to your question. Rules differ all over the world and I'm in Lotus Land.