Elizabeth Palmer was a communications officer aboard the USS Enterprise (NCC-1701) in the 2260s. In 2267, she was on duty during the encounter with the planet killer. (TOS: "The Doomsday Machine") In 2269, she tried to contact the stolen ship Aurora. (TOS: "The Way to Eden")
Star Trek Continues
Palmer served alongside Nyota Uhura in communications right until the final mission of the Enterprise. (Star Trek Continues)
38589 Years Difference
Palmer was on duty when the Bibliothèque arrived to assist the Enterprise.
Later, she was one of 47 to survive the destruction of the Enterprise at the hands of a rogue faction of the Adeptus Mechanicus.
After the Starfleet crew's mission to restore the derelict USS Miranda and Enterprise (NX-01), Palmer chose to join the Space Wolves as an assistant alongside Marlena Moreau. (38589 Years Difference)
Palmer (Lieutenant) article at Memory Alpha, the canon Star Trek wiki.
Elizabeth Palmer article at Memory Beta, the non-canon Star Trek wiki.