仕 means 'to serve as an official' (from the imperial examination era - passing the 科举 (kējǔ, civil-service exam) put you on the 仕途). Today the word still implies the bureaucratic/political career track specifically, not business or academic success.
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Formal/literary. In casual conversation about office careers people use 事业 (career) or 工作; 仕途 specifically evokes climbing the government ladder.
