The brassiere (or bra) was an article of clothing that covered, supported, and elevated the breasts of a mammalian humanoid. Long-standing traditions of the Human civilization dictated this to be underclothes and as such, the appearance of the bra was considered to be a private matter.
History and specifics[]
While Katalya Tremain and Spock were stranded on the planet Arachnae after the deaths of the rest of their landing party, Tremain removed her Starfleet uniform in front of Spock. She then chastised him for noticing the transparent nature of her brassiere. (TOS novel: Vulcan!)