Paul Rice attended Starfleet Academy with fellow Starfleet officer William Riker. Riker remembered him as a confident man, almost to the point of arrogance; he managed to get away with this trait because he had a tendency to be right. When he took his final test in one of his courses at the Academy, there were three options available; Rice ignored them, and came up with his own solution. As a result, he was awarded the highest score for the test, which was still in use at the Academy, albeit with four available solutions. Based on this profile, Counselor Deanna Troi reasoned that such a man would have a tendency to fight a battle, as opposed to retreat from one.
In 2364, the Drake was assigned to Minos to discover why the planet had suddenly become unpopulated. The Drake was apparently destroyed by one of the weapons constructed by the people of that planet, a weapon which almost destroyed the USS Enterprise-D a short time later.
When Commander Riker, as the Enterprise first officer, beamed down to Minos, he encountered who he initially believed to be Paul Rice. Sensing something was wrong, Riker gave the name of his ship as the USS Lollipop in order to test Rice. Riker soon determined that he was speaking with a holographic version created by the automated weapons unit Echo Papa 607, whose purpose was to extract information from him. Upon realizing Riker had discovered the ruse, the hologram of Rice disappeared. (TNG: "The Arsenal of Freedom")
Paul Rice was played by actor Marco Rodriguez.
The script for "The Arsenal of Freedom" describes the hologram of Rice as, "trim and neat, a man of Riker's age with a military bearing. He is businesslike and calm, and acts as if this kind of meeting, under these circumstances, is perfectly normal." 
Paul Rice also has a card in the Alternate Universe series of the Star Trek Customizable Card Game, which also contains an "easter egg" showing the words "daed si luap" ("Paul is dead" backwards) - a reference to the urban legend that Paul McCartney died in a car accident in 1966, and while The Beatles covered up his death and found a lookalike-soundalike replacement, numerous songs played backwards (as well as regular lyrics and images of the group) contained various clues revealing the truth.