Dear BD, English teacher:
You wrote:
> Is this the proper use of the word that?
>
> A typical noir plot revolves around a female character THAT hires
> a detective.
>
In this sentence with two possible antecedents (“plot” and “character”) “who” would be more precise. “That” normally refers to people only as groups or types. Usually it refers to things. See “That/Which/Who” in Grammar Slammer or https://www.englishplus.com/grammar/00000255.htm.