I had a disagreement with a friend over this question.
Which choice is the right one?
I have an interview for a teaching _____ at the university.
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Post is correct.
Is something you will need to possess in order to secure the post.
Is something you establish yourself, owing to the nature of jobs you gain skill at, apply for and are successful at winning.
Likewise a career is something you build yourself, an interviewer can not award you a career, although they may be able to offer you a career opportunity. You still need to build the career yourself, by the degree to which you are successful at your job, and the career moves you make (if any).
Refers to a single job posting and this is what you are being interviewed for when you sit a job interview.