Jim,
If you try a marine supply you’ll find no shortage of teak cleaners, brighteners, and preservative oils. I’m not familiar with who you have in your area, maybe West Marine.
Cleaners are usually a 2 part affair, Oxalic acid and a neutralizer. Not a particularly fun job to do. Make sure you wear plenty of protection as the chemicals are harsh on you as well as the wood.
Follow the directions. After cleaning, you’ll want to put on several coats of teak oil.
It will need constant care if you want to keep it in Palm Beach condition. It’s a lot easier to start liking the aged appearance. :gar-La;
Stephen