The central issue in Kirk's brag to Korob is that the Starship Enterprise's personnel and equipment "could manufacture a ton" of precious gems. This suggests that the Enterprise has an industrial process (like a super-advanced 3D printer) that, given the product's specifications and that they do not exceed the machine's capabilities, can "manufacture" many different articles, including clothes, food, machine parts, medical items, blankets, etc. Another possibility, quite a bit more advanced, would be that the TOS-era starships did have some early kind of replicator technology, maybe not food replicators, but maybe a room-sized industrial replicator for fabricating needed parts and other necessities while on the frontier. Either way, the technology would be very limited, possibly crude by TNG standards, but still a useful part of a starship's standard equipment.