Sort of like The Outer Limits' "The Premonition", this was a story that included a time-slow-down mechanism set on a military base (at least partially). I was sure it was The Outer Limits but I've looked at all episodes and it must be some other show. Very much that kind of production and timeframe. 1960s - possibly early 70s.
It appeared to a small group of people that time for the rest of the world was frozen but actually was just moving very slowly. But it turned out that it was the small group of people that were moving at a hyperspeed - so fast that they were invisible to the rest of the world. The show had perspectives from both sides. The only clue to the rest of the world was a kind of buzzing sound they would hear when the smaller/faster group or individual was near.
I don't remember the story, though it must have been an episode of some sci-fi show. Apologies for being vague but this was the 60's, I was young, etc. but these memories are very specific.