One meaning of incumbent is a person who holds a particular position or place. In this sense "incumbent" fits your sentence, but it would not commonly be used that way in English. Chief Financial Officer, Chief Accountant, Comptroller (not controller) are some terms we use.
I'm reopening this thread because I'd like to know if the use of 'incumbent' outside bureaucratic-governmental and political contexts may sound contrived. For example, I have found some relevant instances of 'incumbent Project Manager', like this one from a job description:
The result of the inventory will determine if the following addition areas of BCD/DR are continued with the incumbent Project Manager
Would it sound more natural to say 'current Project Manager' here or gives 'incumbent' a different nuance (or a differerent meaning altogether) to the sentence?