She was an architect, and Trip noted that she went on a lot of trips to oversee and present projects.
In March 2153, Elizabeth was killed at her home in Florida in the Xindi attack on Earth, which also claimed the lives of seven million other people. Trip lost a lot of sleep over this, and was helped to get over his sister's death by crewmate T'Pol, using Vulcan neuro-pressure. Even Andorian Commander Shran expressed his condolences to Trip, after having been told by Enterprise NX-01 captain Jonathan Archer. (ENT: "The Expanse", "The Xindi", "Proving Ground")
Background information Edit
During a dream sequence in "The Xindi", two versions of Elizabeth Tucker appear – a child version who was scripted to be eight years old, and an adult version who was scripted as being "in her early 20's." In the same script, these depictions of the character were both described as "wearing a blue dress," which matches how she is represented in the final version of the episode.
Trip actor Connor Trinneer once implied that he believes Elizabeth Tucker was used to symbolize the victims of the September 11 attacks, saying, "I think that Trip’s mourning his sister had a lot to do with that grieving process." 
The novelization of "The Expanse" and "The Xindi" (entitled The Expanse) characterizes Elizabeth Tucker as having a conservationist mentality, alternate to her brother's interest in space, and portrays her as scuba-diving off the Florida Keys at the time of her death.