Pomet is a member of Kelsey's gang of trilithium thieves aboard the deserted Enterprise-D in Starship Mine, who is put out of action by Jean-Luc Picard with a crossbow.
Pomet appears in the sixth-season episode Starship Mine. He is one of the armed party that slips aboard the Enterprise while it is empty for a baryon sweep at Arkaria Base, planning to drain trilithium resin from the engines.
Once Picard escapes their custody, Pomet is among those sent to hunt him through the Jefferies tubes and corridors with their energy weapons disabled by the sweep's precautions. Picard arms himself from Worf's quarters and brings Pomet down with a crossbow bolt treated with a sedative.
His loss is one more step in the steady reduction of Kelsey's team, which ends with her fleeing the ship alone.