An incumbent resident as a longtime or current resident of a home or neighborhood is a jargoned use of the word not yet acknowleged by dictionaries, but current in such academic disciplines as demography, urban planning, and population studies in both the UK and US.
For example, if the elderly person is head of household, we might assume that they are the incumbent resident, and that the children have moved in with their parent. — Centre for Longitudinal Study Information and User Support, Department of Population Studies, London School of Hygiene & Tropical Medicine.
Located in the grounds of Great Brampton House, residents stay in Social Sculpture, a small building designed to accommodate one person. … The incumbent resident is reliant on the previous resident to have washed the linen, cleaned and tidied. — Arts Council, England, 2014.
“Because my research is concerned with the effect of gentrification on incumbent resident health, it is inextricably linked to questions of rising rent and the displacement of low-income residents,” she said. — Brown University Population Studies and Training Center, 7 Sept. 2017.
Gentrification encourages redevelopment and revitalization while also increasing the risk for involuntary incumbent resident displacement. — Leah G. Neal, “Developing a Practical Ideal Type Gentrification Effects Mitigation Program: A Study of Austin, Texas,” Texas State University, 22 May 2013.
The late 20th c. use of incumbent in legal and commercial contexts offers some insight in the steps toward incumbent resident. An incumbent owner doesn't necessarily hold an office, but does hold title to real property or the majority of voting stock in a company. Here, the incumbent owner currently holds a broadcasting license threatened by a rival:
In the two-step procedure, groups actually seeking to win the license for themselves—rather than forcing the incumbent owner to improve service through a petition to deny, could not obtain a hearing for a competing application until they had first proved that the incumbent's performance was seriously below the standards required by law. — Broadcast License Renewal Act: Hearings before the Subcommittee on Communications of the Committee on Commerce, United States Senate, 1974.
An incumbent owner is contrasted with a successor in labor law:
But they do go off on the idea of whether the successor owner is really a different owner than the incumbent owner. — House Subcommittee on Labor-Management Relations, 8 Mar. 1983.
While under Burns, a successor employer is ordinarily free to set initial terms of employment without bargaining with the incumbent owner, that privilege is forfeited when an employer discriminates in unlawfully refusing to hire the predecessors employees. — Decisions and Orders of the National Labor Relations Board v. 347, 11 Aug. 2008.
Incumbent businesses are existing, established firms, contrasted to new or entrepeneurial ventures:
South Korea is said to be representative of a socalled Asian model of development (a misleading moniker, given the vastness and diversity of the Asian continent) based on government support of incumbent business, not entrepreneurial challenges to them. Philip Auerswald, The Coming Prosperity, 2012.
as this author conveniently explains:
Thus, the nurturing of existing (incumbent) business life and the creation of favorable incubation conditions for new business initiations. — Harvey Lithwick, Yehuda Gradus, Developing Frontier Cities, 2013.
Incumbent residents are established — they were there first — before the gentrifying “urban pioneers” moved in, whether they are incumbent owners worried about rising property taxes or renters concerned about rent hikes in a gentrifying neighborhood.