In 2365, she had recently graduated from Starfleet Academy and was transferred from Starbase 173 to the USS Enterprise-D to serve under Lieutenant Geordi La Forge. It was Gomez's goal to serve on the Enterprise-D for years. La Forge expressed appreciation for her excitement, and mentioned that she could be of better service if she learned to relax a little. Shortly before that, she had accidentally spilled her hot chocolate on Captain Picard. (TNG: "Q Who")
Background information Edit
The script for "Q Who" describes Gomez as "a young twenty five to twenty eight year old ensign -- who has newly arrived on the Enterprise. She is very energetic, and enthusiastic in an open and ingenuous way, which is both appealing and refreshing." 
In Pocket Books' Star Trek: Starfleet Corps of Engineers series, Gomez appears (in the post-Dominion War era) as the executive officer of the series ship, USS da Vinci, with the rank of commander. In the Star Trek: Destiny novels, Gomez had been made captain of the da Vinci. In Star Trek Online Gomez became head of the Starfleet Corps of Engineers prior to 2401, and resigned the position that year to be replaced by Miles O'Brien.