All the equipment, such as a mat, will be provided for you but some people wish to bring their own. Some also like to bring a small towel to support their head and some water as well.
It is recommended you wear comfortable clothes that have some stretch/give in them. Ideally don’t wear baggy clothes as it is useful for Kate to see how you are using your muscles. You do not need to worry about footwear as Pilates is done without shoes on.