Using a renewable resource - such as wind, solar, and hydropower - to generate electricity does not deplete that resource. There will always be consistent sunlight shining on the Earth's surface. After turning sunlight into electricity, there is still an infinite amount of sunlight to turn into electricity in the future. That is what makes solar power such an incredible resource.
While the current electricity mix in the Cayman Islands is still made up largely of fossil fuels like oil and gas, renewable energy sources like solar are steadily becoming a larger part of its energy profile.