When you let someone back in after they've left, you readmit them. Most museums and movie theaters will readmit you later if you save your ticket.
If you leave an outdoor concert to grab a sweater from your car, they'll readmit you when you show the ink stamp on your hand. A hospital might readmit a patient who's been released only to have their symptoms get much worse. And colleges often readmit students who've taken a leave of absence. Readmit uses the "again" prefix re-, with admit, from the Latin root admittere, "to allow to enter."