late 15c., "a guide," from Anglo-French directour, French directeur, agent noun from Latin dirigere "set straight, arrange; give a particular direction to," from dis- "apart" (see dis-) + regere "to direct, to guide, keep straight" (from PIE root *reg- "move in a straight line").
Corporate sense of "one of a number of persons having authority to manage the affairs of a company" is from 1630s; theatrical sense of "the leader of a company of performers" is from 1911.
word-forming element used in forming nouns from Latin words ending in -atus, -atum (such as estate, primate, senate). Those that came to English via French often arrived with -at, but an -e was added after c. 1400 to indicate the long vowel. The suffix also can mark adjectives formed from Latin past participles in -atus, -ata (such as desolate, moderate, separate); again, they often were adopted in Middle English as -at, with an -e appended after c. 1400.
<a href="https://www.etymonline.com/word/directorate">Etymology of directorate by etymonline</a>
Harper, D. (n.d.). Etymology of directorate. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/directorate