A harpoon gun was a gun capable of firing harpoons.
The harpoon gun used by the Anomaly research team was a large, rifle-like gun, with one large, metal harpoon at the end that could be fired at creatures and enemies. Some versions of this harpoon gun also possessed a rope connecting the harpoon and the gun itself, with which to bind harpooned creatures to nearby structures and limit their movement.
When Nick Cutter was assigned to swim through an underwater Anomaly into the Cretaceous in search of Helen Cutter, Stephen Hart gave Cutter a harpoon gun, as a defensive weapon against any predators in the Cretaceous, and Cutter subsequently took the harpoon gun through the Anomaly with him. When Cutter was attacked by a Mosasaur in the Cretaceous bay while trying to return through the Anomaly, he fired the harpoon gun at the Mosasaur, but the harpoon bounced off the creature's skin and only slowed it down due to the Mosasaur's tough armour.
The harpoon gun was among the weapons in the armoury that Oliver Leek showed to Connor Temple and Abby Maitland, but it was useless like everything else there since they were looking for something that could clear Precambrian fog.
Nick Cutter, Connor Temple and Abby Maitland took a harpoon gun with them when they went out onto a canal in the Isle of Dogs searching for creatures. When Abby was taken by a Mer Creature, Connor took the harpoon gun to try and kill the Mer, but Cutter ordered Connor to lower the weapon due to risk that he could end up killing Abby with it.
When Stephen was sent to a beach to neutralise a Silurian Scorpion, he took a harpoon gun with him as a weapon against the creature. Using the harpoon gun, Stephen managed to harpoon the Scorpion and bind it to a pier, and left it to be captured by the Anomaly Research Centre.