An agricultural colony, farming colony, or farmworld was a colony developed for the purpose of agriculture.
Omicron Ceti III hosted an agricultural colony. (TOS: "This Side of Paradise")
In 2267, Captain James T. Kirk noted in his captain's log that locating survivors of Berthold ray exposure there was most unexpected.
Later, Leslie mentioned in a biology report to the captain that despite the apparent fertility of the soil, oddly enough, they hadn't planted much acreage beyond what was needed for their own survival. (TOS: "This Side of Paradise")
Gault was a farming colony. There was also a farming colony on Coltar IV. (TNG: "Heart of Glory", "We'll Always Have Paris")