Changing careers is indeed an option on the phone and also on the computer. There is no need to quit your current job first.
Phone: Find a Job from the Business menu. If you already have a job, you'll get a popup dialogue after you choose a new career that says something like, "Should Beverly switch activities to Mailroom Technician? She will quit her current position of Orderly upon accepting to do a new activity."
Computer: Find a Job from the Career... menu. You'll get the same popup.
NOTE: I'm using the PC version. It's possible that the console version is different.
I had to stop going to work to change my job because I don’t have any options on my phone for it and paying bills. The only options is travel and browse web
