A lab coat was a piece of clothing sometimes worn by medical doctors and scientists.
Denobulan and Human doctors with the Interspecies Medical Exchange during the 2150s wore civilian clothing beneath stark, white lab coats at locations including Cold Station 12. These lab coats featured pockets on the left chest and assignment patches on the left sleeve. (ENT: "Cold Station 12")
Dr. Beverly Crusher wore a blue lab coat during her time as chief medical officer of the USS Enterprise-D in the 2360s and early 2370s. (Star Trek: The Next Generation)
In 2372, Dr. Honey Bare wore a lab coat in the Julian Bashir, Secret Agent holonovel. (DS9: "Our Man Bashir")
White lab coat, early 2370s