pre-admission (n.)

early 15c., "acceptance, reception, approval," from Latin admissionem (nominative admissio) "a letting in," noun of action from past-participle stem of admittere "admit, give entrance; grant an audience," of acts, "let be done, allow, permit," from ad "to" (see ad-) + mittere "let go, send" (see mission).

The meaning "an acknowledging" is from 1530s. The literal sense of "act of allowing to enter, admittance," is from 1620s. As short for admission price, by 1792.

word-forming element meaning "before," from Old French pre- and Medieval Latin pre-, both from Latin prae (adverb and preposition) "before in time or place," from PIE *peri- (source also of Oscan prai, Umbrian pre, Sanskrit pare "thereupon," Greek parai "at," Gaulish are- "at, before," Lithuanian prie "at," Old Church Slavonic pri "at," Gothic faura, Old English fore "before"), extended form of root *per- (1) "forward," hence "beyond, in front of, before."

The Latin word was active in forming verbs. Also see prae-. Sometimes in Middle English muddled with words in pro- or per-.