In some cases, especially among recent grads, a job applicant will be looking for a one year gig to get his foot in the door somewhere and won’t be particularly concerned with where this job may lead. Some hiring managers recognize that — many agents have verbal agreements with their assistants that after a year on the desk, they’ll help a rockstar assistant find another job. If you know that the job you're applying for is just a stepping stone, don't even bother with the room for growth question.
However, as you develop your skills, you'll want to look for a more satisfying career trajectory. You’ll be interviewing at companies that you’re passionate about and hope to stay at for several years. At the more senior levels, asking about growth potential is a pretty standard question, but if you’re applying for an assistant position, you have to be a little more careful. In many cases, hiring managers are looking for someone who cares about the company and wants to grow into a more advanced role down the line, but sometimes when an executive hires an assistant, he wants just that. He's looking for someone who will be able to manage the administrative parts of the job and can make his life easier, not someone who gets so caught up in giving script notes that he forgets to answer the phone. It's not always easy to assess exactly what the hiring manager is looking for, so if you're genuinely interested in long-term employment that eventually goes beyond the assistant level at a particular company, you'll need to handle any questions about upward mobility delicately.
So, how do you ask about potential growth? You could start by inquiring how long people typically stay at the company. This may be enough to prompt an answer about a potential promotion down the line, but at the very least, it will give you a sense of whether or not employees at the company are happy. Alternatively, you could be a little more straightforward and ask if there’s room for growth in the department or if assistants typically get promoted within the company. If you choose this route, add a caveat that you know you’re being hired as an assistant and are ready and willing to spend a couple of years on an entry-level desk. If you can get this across while also demonstrating that you are enthusiastic enough about the company that you’d be the type to go above and beyond and eventually earn that promotion, you’ll sound like a great candidate.