Once you have build the community centre, you are able to send your Sims there to learn new hobbies, including karate, ballet and woodworking. Simply send one of your pre-teens there, and make them practice karate. There are a few options, and of course the shorter timed sessions will yield more xp for them and make them level up quicker, but you will need to babysit them more. Whichever sessions you use, eventually the kid will get to Black Belt. Just ensure you don't start a new hobby as this will reset their rank.