Ability suppression is the gift to suppress other vampires' abilities. So far, the vampire Royal is the only known individual to possess this ability.
"I can stop anyone from using their gift. Stop them right in their tracks." - Royal explaining his gift to Bella.
Royal has the ability to stop anyone for using their gifts. Exactly how his power works is unexplained, but he can project a shield away from himself that stop others from using any gifts inside of it. His range is limited.