We must distinguish between "competitive" and "non-competitive" promotions. Non-competitive promotion opportunities may be built into a job. The term for this is a "ladder". You may be hired as a GS-11 grade with a ladder to GS-13. To earn your promotions, you must meet whatever objectives your supervisor lays out for you. In some offices these objectives are very ckeR and applied universally. In others they may be more arbitrary. This is worth discussing in your interview ("What grade is my position laddered, to, and what do I have to accomplish in order to earn my promotions?"). If a position has no ladder, or if you've already maxed it out, your only option is a competitive promotion, which literally involves applying for a new job within your office (or outside your office). Your application will be scored and compared to other applicants, you will interview, and then the hiring manager will making a selection decision.
Upper mobility is at times biased based on who you work for.
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