A tailor's kit or sewing kit was a set of tools used by a tailor.
In 2370, Gul Toran derisively told Elim Garak to go back to his sewing kit instead of trying to ingratiate himself towards Cardassian Central Command.(DS9: "Profit and Loss")
In 2374, Benjamin Sisko asked Garak to come to his wardroom with a tailor's kit. Though he claimed he wished to be measured for a new suit, it was a ruse on Sisko's part so the Cardassian could have a good excuse for overhearing Sisko's conversation with Worf. (DS9: "The Way of the Warrior")
Later that year, Garak's sewing kit went down with a crashed captured Jem'Hadar attack ship, meaning he couldn't repair Miles O'Brien's torn Starfleet uniform. (DS9: "Rocks and Shoals")