The question itself doesn't help as it's not completely idiomatic either way.
You take up karate (not karate class).
You follow a course (possible but a bit dated/stiff).
a (or the) karate class (not karate class)
Here are some possible sentences:
- She wanted to take up karate.
- She wanted to start karate classes.
- She wanted to follow a karate course.
Hope this helps