"the prior incumbent" is correct and usable in written English. It is usually used to refer to someone who previously held a job or position, such as a politician or executive, and can be used in both formal and informal contexts. For example, "The prior incumbent of the Senate seat was defeated in the recent election.".
The prior incumbent was Rick A. Lazio, a Republican who ran against Hillary Rodham Clinton for the Senate in 2000 and declined to try a comeback.
Under state law, the successor had to come from the same party as the prior incumbent.
I voted for him because he is a Democrat who supported Obamacare, raising the minimum wage and the draw down in Iraq, and because the prior Republican incumbent was way too comfortable with the Tea Party (which, in my mind, mixes hypocrisy and idiocy in equal measure to advance its politics of "No").
Why the prior neglect?
The prior record holder?
In case of an open-loop differential game the incumbent overinvests prior to the entry occurrence.
Prior to the election, the office-motivated incumbent party (IP) can influence the degree of disagreement through policy experimentation — a public signal about a payoff-relevant state.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union