Is it good or bad to use a martial art that you're already good at, in a martial art you're just starting?

I think it's impossible not to import a bit of your old style into your new style. There's nothing wrong with that, but you have to try to go into the new art as a blank slate as much as possible. Don't show off, and try to use techniques from the new art. Also, probably a good idea to mention that you have a black belt in another art...