To answer the question, it may be helpful to consider what is meant by "stable". Keep in mind that I'll be writing this for a pharmacist in the USA.
Pharmacists tend to have wage and employment stability based on general market forces that are mostly outside of the control of an individual. Most pharmacists can expect wages in the six figures when they are first hired. Layoffs for most positions are also rare, so the positions tend to be stable in those regards.
However, there are many ways to specialize within pharmacy and many positions require education to gain experience in those specialties. You can expect to do a residency after college, which may last 1-2 years and may require you to move in order to be at a location to learn. Upon completion of the residency, you may need to move again to a location that is hiring. In this way, pharmacists often don't have stability within their early career depending on which specialty may be chosen.
Pharmacists may not have much stability in their day to day work. Many hospital and community retail sites will be open 24/7 and the scheduling of work hours may not be stable. There are positions at other locations which have more stable daily schedules, such as ambulatory care, infusion centers, or industry. The day to day work often varies and changes over time. Healthcare is always changing and pharmacists are required to keep up with new knowledge and apply it in their positions. I would consider this to be a requirement of the job, and if you are not comfortable with changes at work, then pharmacy may not be a good position for you.
With all this in mind, what can you do to have a stable career? First, consider which aspects of stability are important to you. When you're in pharmacy school, be sure to consider your intended specialty carefully. Network with those who are in the positions you are considering and ask about these types of concerns.
1. Obtain a degree in pharmacy: You need to complete a Doctor of Pharmacy (PharmD) degree from an accredited pharmacy school.
2. Get licensed: You must pass the North American Pharmacist Licensure Examination (NAPLEX) and the Multistate Pharmacy Jurisprudence Exam (MPJE) to be licensed to practice pharmacy in your state.
3. Gain experience: Consider working as a pharmacy intern or technician to gain experience before becoming a licensed pharmacist.
4. Choose a career path: There are various career paths in pharmacy, including community pharmacy, hospital pharmacy, clinical pharmacy, and research pharmacy. Choose a path that aligns with your interests and goals.
5. Continue education: Keep up with the latest developments in the field by attending continuing education courses and staying informed about new medications, treatments, and technologies.
6. Network: Build relationships with other healthcare professionals and pharmacists to expand your knowledge and career opportunities.
By following these steps, you can have a stable living as a pharmacist.