Admiral Moore was a 24th century Starfleet flag officer stationed at Starbase 73.
In 2365, Moore met with Captain Picard to discuss a recently discovered SOS call located in the Ficus sector. Moore subsequently ordered the USS Enterprise-D to conduct a mission to investigate the mysterious call. (TNG: "Up The Long Ladder")
This character was only mentioned in dialogue.
According to an early draft of the script, Admiral Moore was given the first name of "James", this reference, however, would not be made in the finished episode.