active word-forming element in English and in many verbs inherited from French and Latin, from Latin de "down, down from, from, off; concerning" (see de), also used as a prefix in Latin, usually meaning "down, off, away, from among, down from," but also "down to the bottom, totally" hence "completely" (intensive or completive), which is its sense in many English words.
As a Latin prefix it also had the function of undoing or reversing a verb's action, and hence it came to be used as a pure privative — "not, do the opposite of, undo" — which is its primary function as a living prefix in English, as in defrost (1895), defuse (1943), de-escalate (1964), etc. In some cases, a reduced form of dis-.
Old English hyrian "pay for service, employ for wages, engage," from Proto-Germanic *hurjan (source also of Danish hyre, Old Frisian hera, Dutch huren, German heuern "to hire, rent"), of uncertain origin. Reflexively, "to agree to work for wages" from mid-13c. Related: Hired; hiring.
<a href="https://www.etymonline.com/word/dehire">Etymology of dehire by etymonline</a>
Harper, D. (n.d.). Etymology of dehire. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/dehire