Being brilliant can be an asset, but knowing how to execute a strategy—that's what will make you a rising star in an organization. Many strategies fail in the execution stage—even though the original idea was a winner. That's because big ideas are much easier to come by than the long, hard haul of building a service or product.
If that weren't the case, there'd be myriad knock-offs for every business success. Who can't walk into a McDonalds and observe their big ideas in action? Yet few are able to replicate this operationally.
Pay attention to the people in your organization who know how to execute an idea successfully, and see what they have to teach you.