Casual, comfortable resort and leisurewear is acceptable everywhere. There are a few restaurants requiring more dressy attire, which would include a shirt with collar and pants for men. You will most likely live in your swimwear at the Villa and sportswear is enough to get around on island during the day. Mind that you could need a light sweater or wrap for cool evenings. You will not need a jacket or tie in any of the restaurants or clubs, although the casino prefers smart casual dress.
Most importantly remember that sunglasses and a hat are a must. Even on a cloudy day, it is very easy to get a very bad sun burn, especially if you have sensitive skin. The Villa stocks a variety of different sunscreens for your use.
Please keep in mind that the Turks and Caicos Islands are quite religious. So if shopping in public after you have just come from the beach please note, that wearing swimwear only is not really appropriate. Thus covering up with shorts and a shirt or a beach wrap is indeed respectful of the culture. Also nude sunbathing is not permitted on any of the public beaches, as public nudity is illegal. The beach immediately outside of Club Med has traditionally allowed topless bathing, as long as children are not in the vicinity. However, at the Villa you make the rules!