The existing tower replaced the wooden one in 1853, but some of the guards' duties were taken over by the police in 1859, others by the fire brigade in 1866. The city guard system continued until 1922, when the last guard retired. The tower is now used as a museum and a view point.
The linked web page is in norwegian, but there are a couple of pictures. The main page stavangerguiden.com does have quite a lot of information in english.
I have made a travelogue with pictures of the view from the top of the tower.


