Old English rædere "one who counsels; person who reads aloud to others; lector; scholar; diviner, interpreter," agent noun from rædan (see read (v.)) in its various senses. Compare Dutch rader "adviser," Old High German ratari "counselor." The Old English fem. form was rædistre. Meaning "a reading book for schools" is by 1789.
word-forming element meaning "quality, condition; act, power, skill; office, position; relation between," Middle English -schipe, from Old English -sciepe, Anglian -scip "state, condition of being," from Proto-Germanic *-skepi- (cognates: Old Norse -skapr, Danish -skab, Old Frisian -skip, Dutch -schap, German -schaft), from *skap- "to create, ordain, appoint," from PIE root *(s)kep-, forming words meaning "to cut, scrape, hack" (see shape (v.)). It often forms abstracts to go with corresponding concretes (friend/friendship, etc.).
<a href="https://www.etymonline.com/word/readership">Etymology of readership by etymonline</a>
Harper, D. (n.d.). Etymology of readership. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/readership