Most accommodations in Provo have washers and dryers in the units, so pack light. You can wash your clothes conveniently at your whim and dry swimsuits before repacking. If your resort doesn't offer laundry facilities or a laundry service, you'll find a dry cleaner/laundry facility next to Beaches on the Lower Bight Road. There is also a dry cleaner in the complex just south of Graceway Gourmet IGA, as well as one on the extension of Leeward Highway.
If you travel with a carry-on, remember that airlines allow only 3-ounce bottles of liquids. Don't worry: it's not too expensive to buy sunscreen at the Graceway IGA supermarket. There's really not a huge bug problem in the Turks and Caicos, but sometimes after a rain or at dusk you might get a bite or two, so you will end up needing to bring or buy some repellent.
Almost all the resorts and villas have hair dryers and give you shampoo, conditioner, and a small box of laundry detergent. Check ahead to be certain. "Bring half the clothes and twice the money"—words to live by.