One of the many questions job seekers ask when they are in a job interview is about opportunities for promotion or advancement. Normally, asking about opportunities for advancement is a good thing because it shows ambition and a desire to stay with the organization–unless there is just no opportunity for that in a teeny tiny nonprofit, for instance.
You can guess whether it’s a good question to ask by downloading the 990 tax return (if it’s a nonprofit) from Guidestar.org… and/or asking first about how many staff there are. If it’s a founder-driven nonprofit with a paid staff of 3 and otherwise volunteer-based, chances are good that you are not going to become the executive director tomorrow (though you never know).
You can also rephrase the question and make it more neutral by asking about opportunities to learn and grow with the organization–which is something you might want to do even if there’s no obvious career track established. So, for instance, if it’s a tiny nonprofit and the only way to move up is if someone else leaves, you still might progress with the organization by taking on new roles, gaining training or exposure to new skills, building up a new program, etc., and eventually be promoted even when there is no official, formal career promotion pathway.