As a member of the New York Police Department, Elisa Maza is assigned a service pistol. Throughout the course of the series, she has lost a fair number of these weapons. Greg Weisman has noted on the (almost funny) frequency of her tendency to lose them, musing that she has probably blamed David Xanatos when trying to account for the lost weapons. 
Instances Of Lost And/Or Destroyed Guns
While Elisa did not lose or have this gun taken away from her per se, after Broadway accidentally shot her with it, the gun was confiscated by the police and tested for prints. It should be presumed she was assigned a new gun following this incident.
Elisa's gun was taken away from her by Glasses when she was taken hostage. It is unknown if the gun was recovered, or she was assigned a new one.
David Xanatos took Elisa's gun when she aimed it at the Werefox, crushed it, and then politely handed it back to her.
Elisa was disarmed when she was knocked unconscious by the newly upgraded Hyena.
Gargoyles (Marvel Comics)
Elisa seemed quite gun happy in the Marvel comic book. Even to the point of, well, check out the image for yourself.
With the series having done an episode on gun violence, the creative team had to find ways to keep Elisa from shooting anyone with her gun. Using up the bullets against beach constructs of the Archmage and suits of armor in the Hollow Hill during the "Avalon" trilogy was one of the means to comply with Standards & Practices.
According to Elisa, her gun(s) are made of steel alloy with a little bit of iron. ("Ill Met By Moonlight")