The clutch is a part 19th and 20th century Human automobiles.
When Tom Paris crashed his automobile in the Fair Haven holoprogram, he blamed it on a clutch malfunction. (VOY: "Spirit Folk")
The inhabitants of Sigma Iotia II used automobiles patterned after those found described in Chicago Mobs of the Twenties. Captain Kirk managed to operate one of those vehicles after remembering the relationship between the clutch and the gears. (TOS: "A Piece of the Action")
A Grenthemen water hopper is another mode of transportation that has a clutch. (TNG: "Peak Performance")