EDIT:
Some employees are simply happy in their roles, and remain there for years (or even decades) as productive team members. As a manager, your role is to bring out the best in your employees and make sure they are happy, not to force development on them.
There are plenty of valid reasons that a person may not want to move up. Maybe she is turned off by the added responsibility, longer work hours, change in work content, or maybe she just has a real passion for what she does now.
Nonetheless, sometimes long-term career planning can feel like just another mandatory procedure rather than a genuine effort to setup employees for long-term success and happiness. So, understandably, employees don't invest the time to think through career development.
If that is the case, here is an approach which follows the positive practice of coaching. It may help you to discover the employee's hidden passions. I run an online community called Resolve, and this answer was originally created by one of its community members.
For your employee to open up, she might need dedicated time and space
away from normal work meetings. Try setting aside an hour to coach her
specifically on career goals, with nothing else on the agenda. In the
manager/employee relationship, not all employees feel comfortable
delving into their vision for the future, and some might feel
pressured to come up with an answer they think you would like. If you
make it especially clear that you are there to help her grow
professionally by separating the conversation from your normal
one-on-one, that may help her open up.
In the meeting, use these coaching techniques to help challenge your
employee to dig deep into her core motivation.
1. State your intention
For example: "I'm here today to help you come up with a vision for
your future. I'm not attached to what that vision is. I want to
support you to grow professionally, so whatever you want to talk about
is fair game." Tip: Try to genuinely let go of your attachment to
keeping this employee for the long term. Sometimes the best way to get
the most out of people is to support them in making their next move.
Maybe they'll only stick around for 3 years instead of 5, but if they
are genuinely engaged, they'll create a much bigger positive impact
for your company. Read The Alliance by Reid Hoffman if you want to
learn more about this idea.
2. Ask open ended questions from different angles
Examples: "Where do you see yourself in five years? What do you enjoy
most about your work? What do you care about most in life? How does
your work feed your values? What gets you out of bed in the morning"
3. Keep asking questions until she describes her deeper
motivations
For example: "I want to be a role model for my kids," or "I want to be
financially free by the time I'm 50."
4. Now, ask questions and offer guidance to help her articulate a
career plan that will help her accomplish her life goals or serve her core values
Examples: "How do you get there from here? What's your next step? If
that is where you want to be in 5 years, what can you do differently
now to get your moving in that direction?"
After this conversation, she won't just have an idea of her career
plan, she'll have a good sense of what is motivating her to move
forward. Better yet, you'll know her core motivations and can remind
her of them any time you think she needs a boost.