A siege was a type of military action in which a settlement was effectively cut off from the outside world by enemy forces, unable to bring in anything needed.
In Klingon history, Emperor Sompek and ten thousand troops conquered the city of Tong Vey following a lengthy siege. Worf had a holographic program of the incident. (DS9: "Rules of Engagement")
One of Demmas's ancestors led the Ilari rebels against Tieran, laying siege to the Imperial Hall for over a year and burning the city around it to the ground. (VOY: "Warlord")