Thanks for the question. I think that the risk of catching HIV through a manicure is extremely low.
Most good manicure establishments do use equipment that have been sterilized.
However, even if the equipment used was not sterile, the risk of catching HIV is very low. Firstly the manicure tools would need to be blood stained as the virus is present in blood and not on the skin or nail surface.
Secondly, the risk of spread increases with a high viral load and the load in dried blood is much lower as the virus does not survive well outside the body and in the environment.
While the risk of spread of HIV through manicure is low, there is a higher risk of catching other infections like fungus and viral warts if good hygiene is not practised. It is therefore a good idea to check with your manicurist to ensure that only sterile tools are used for you.