There was an episode with a different lifeform living at a slower/faster speed aboard the Enterprise? Would have been in a late 60s episode.
The episode is Wink of an eye. This was episode 11 in Season 3. The description from Wikipedia,
"Wink of an Eye" is a third season episode of the original science fiction television series, Star Trek, first broadcast on November 29, 1968, and repeated on June 24, 1969. It is episode #66, production #68, and was written by Arthur Heinemann, based on a story by Gene L. Coon (under the pen name Lee Cronin), and directed by Jud Taylor.
In this episode, normally invisible time-accelerated aliens take over the Enterprise and attempt to abduct the crew for use as "genetic stock".