高升 is the polite, congratulatory word for a promotion — you say it to the person being promoted (恭喜高升) or about them in a warm tone. For a neutral description, 升职 (shēngzhí) is more common in HR-style writing.
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Slightly formal and congratulatory. In casual speech among peers, 升职 or 升官 are more neutral; 高升 carries a whiff of ceremony, often used half-jokingly among friends.
