A scarf was a piece of fabric which was usually worn around one's neck for warmth or fashion. In Elim Garak's opinion, a nice scarf could go a long way towards completing an outfit. (DS9: "Broken Link") As a child, B'Elanna Torres tried to hide her Klingon cranial ridges using hats and scarves. (VOY: "Faces")
In 2371, when Gathorel Labin offered to have a dress made for Kathryn Janeway out of an exotic material from Dedestris, she declined the generous offer and suggested a scarf instead. After she chose another material, he said it would bring him more pleasure than her to see her wearing it. (VOY: "Prime Factors")
Quark's business associate Tiron wore a scarf. (DS9: "Meridian")
Kathryn Janeway wore a red-silver scarf when she posed as a prostitute in the Mokra Order prison. (VOY: "Resistance")
A scarf could be worn around the head, to become a head scarf. In 2258 of the alternate reality, another head scarf was worn by Amanda Grayson shortly prior to her death. (Star Trek)
Commissioner Nancy Hedford wore a head scarf in 2267 while being taken to receive treatment for Sakuro's Disease. (TOS: "Metamorphosis") An extremely aged Arlene Galway wore a scarf around her neck. (TOS: "The Deadly Years")