Star Trek: 10 Things You Didn't Know About Warp Drive
4. Warp 10 In The Original Series
At the time of the Enterprise's famous five-year mission, the galaxy operated on a different warp scale to that which was used from the Next Generation onward. For example, it was possible for ships to travel in excess of warp 10 without occupying every point in the universe instantaneously, though it was still considered an unsafe velocity.
The Orions routinely travelled at these speeds as, according to Spock at least, they were unconcerned with safety. Modifications to the Enterprise allowed it to travel in excess of this speed as well, including the changes made by the Nomad probe, and by the Kelvans as well.
Perhaps the greatest sustained velocity observed by the Enterprise at this time was that of Karla-five in The Counter-clock incident. Thanks to the extreme time dilation effects of a black hole, and her own natural reversed universe, her vessel was recorded travelling at warp 36 - a speed that was theoretically impossible at the time.
Generally, starships kept their speed below the warp 10 barriers for the safety of ship and crew, though they were, at that time, capable of breaking this speed limit.