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 such as 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; Star Trek Generations)
In 2372, Dr. Honey Bare wore a lab coat in the Julian Bashir, Secret Agent holonovel. (DS9: "Our Man Bashir")
By 2380, the Caitian Starfleet officer Dr. T'Ana wore a light blue lab coat in her role as chief medical officer of the USS Cerritos. (Star Trek: Lower Decks)