I would like to raise my rates, but keep old clients at their current rate. Can this be programmed?

Unfortunately, there's no way to automate this. You could send a message to all your existing clients that you are raising your rates for new clients but will honor your old rate for them but explain that you have to manually adjust it before confirming the booking each time. It's a pain, but at least that way you won't scare them away when they see your new rate.