What is the official star trek story of what happened to Crusher when Polaski took over, and why did she come?
Crusher was invited to reapply the following year, took the exam, and was accepted into the Academy where he joined an elite group of cadets known as Nova Squadron. His involvement with this group led to his losing academic credits (The First Duty), when a squadron-mate was killed attempting a dangerous and prohibited flight maneuver and, under pressure from the team leader Nick Locarno, Crusher abetted the squadron's efforts to cover up the truth. Although the crew's intervention and Crusher's own testimony saved him from expulsion, all of Cadet Crusher's academic credits for the year were canceled and he was required to repeat the year and graduate after most of the rest of his class. He remained in the Academy thereafter until the Traveler re-contacted him, whereupon he resigned his commission and went with the Traveler to explore other planes of reality
Like the second answerer said,Beverly Crusher left Enterprise to become the head of Starfleet Medical(that was the storyline explanation why Gates McFadden wasn't in Next Gen season 2).Now the exact reason of how Dr.Crusher became head of Starfleet Medical,what she did during her time there,and why she came back to the Enterprise is a story that has never been told(it was never fully explained during the run of Next Gen why she left Starfleet Medical and came back to the Enterprise)!
Gates McFadden was replaced during the second season, and the character of Dr. Katherine Pulaski, played by Diana Muldaur, was added as the USS Enterprise-D's chief medical officer. On the show, Crusher's absence was explained due to her being promoted to head of Starfleet medical. Citing a lack of chemistry between Muldaur and the rest of the cast, McFadden and her character returned to the show from season 3 on, to re-replace Pulaski.
