When you "pursue a career", you try to work in a certain industry.

This phrase is usually followed by "in ___":

I'm pursuing a career in nursing.

When I was in my twenties, I wanted to pursue a career in law enforcement.

You can also put the name of the industry before "career":

If you want to pursue a teaching career, you should take courses in psychology and social science as well as courses in the subject you want to teach.

By the way, a "career" is a long-term set of jobs that you get which are all related to each other. For example, I've had two separate careers in my life: one in teaching and one in publishing. I've had several different jobs in each career.