A carry bag was an accessory used to transport personal effects, such as one's clothing.
Several Akaali used carry bags for their shopping. The apothecary Riaan had a small carry bag placed on her hip where she carried her identification papers and some personal belongings in. (ENT: "Civilization")
Spock used a carry bag to hold his clothing when he took a trip through time from 2269 back to 2237, in order to save his younger self from death. The bag and clothing were provided by the USS Enterprise's wardrobe section. (TAS: "Yesteryear")