Legendarily, Majel Barrett played not only Number One in “The Cage,” and Lwaxana Troi in The Next Generation, but Nurse Chapel as well in the Original Series. There is no specific date when Nurse Chapel joins the USS Enterprise. But it’s not crazy to think she’s been around for a while. Could Chapel have served with Spock and Pike before Kirk took over? In some ways, this makes sense if only because you get the sense that she and Spock have known each other for a long time.
You forgot about him, didn’t you? That’s correct, after Boyce and before Bones, there was nobody’s favorite Star Trek doctor: Dr. Piper. In the second pilot, “Where No Man Has Gone Before,” Piper replaced Boyce as the chief medical officer. This is the only episode with this character, and why Bones ultimately replaces him is the subject of a good amount of non-canonical apocryphal reconciliation.
For instance: In the 1985 DC Comics story “All Those Years Ago,” Bones replaces Boyce after the chief medical officer of the Enterprise but must take a leave of absence since he’s going through a divorce.
Also, Bones’ divorce is the reason given for his absence in “Where No Man Has Gone Before,” in the novel Strangers From the Sky. In all these scenarios, Piper was the short-term replacement for Bones. All of which could mean he’s briefly serving on the Enterprise during the time of Discovery.
In the original series canon, Gary Mitchell was allegedly someone Captain Kirk directly requested for the Enterprise. In theory, there’s no way we could hear about or see Gary Mitchell on Discovery since he’s not really supposed to be on the Enterprise just yet. However, all we know is that Kirk wanted Mitchell on the Enterprise, which possibly means Mitchell was already there and Kirk just wanted to be sure he stayed on the Enterprise.