"To make a career" means to pursue and advance in a particular line of work or profession over a significant period of time, with the intention of achieving success, development, and stability in that field. Full definition
His advice to people thinking of making a career change is simple. (moneysense.ca)
A good agent who makes a career of insurance knows his clients and will be there to make sure important insurance events are not missed. (accuterm.com)
So you have reached the point where you trust yourself enough to make the big and somewhat scary decision of making a career out of freelance writing. (beingauthor.com)