Incumbency is the state of holding an official job — especially an elected one — or the stretch of time while the person holds it. During a mayor’s incumbency, she is the one in office. News and political writing love this word because it names the job-as-held, not just the person. People also talk about an incumbency advantage: voters often pick the person who already has the seat, just because they already have it. Though actually, everyday English prefers simpler words: “while she was mayor,” “in office,” “her time as president.” Incumbency sounds like a report. Older writing also used it for a church post (a priest’s incumbency); younger people almost only meet it in politics. It is not quite the same as a “term.” A term is a set length, like four years. Incumbency is the holding itself, however long it lasts.