they turned on the ARC and wiped out humanity. (Episode 3.3)
Helen Cutter travelled through an anomaly and retrieved the technology from a future time period for Leek. Attached to the heads of the Future Predators, so that Oliver Leek could control them. They weren't used on any of the other creatures he had in his army. (Episode 2.6) The clamp was surgically planted in the skull of the Predator and is operated by remote radio signals. Removal of the clamp caused immediate death due to damage of brain tissue, as shown when Nick ripped it off a Predator's head.
While Leek was threatening Lester, warning that he'd have the Predators kill Cutter, Cutter deactivated the neural clamps by inserting one in a circuit box. The electrical charge short-circuited the device, deactivating them all and freeing the predators from Leek's control. Cutter narrowly made his escape as the future predators descend en masse and tore a screaming Leek apart. (Episode 2.7)
It is unknown whether or not the Neural Clamp was created in the first or second future.
As the Neural Clamp and the Future Predator are both from the future, and the Future Predators in Leek's creature prison were the only creatures wearing the Clamps, it is possible that the Neural Clamp are fitted to only work on Future Predators.
Another unconfirmed theory about the origin if Neural Clamps can be, that Christine Johnson made it during her experiments (similar to one showed in Episode 3.4).