An agricultural colony, farming colony, farm planet, or farm-world was a colony or planet developed for the primary purpose of agriculture.
The planet Bootes III was otherwise known as a farm planet. The farming there was tended by automatic machinery as well as a few Humans, which included Eve McHuron and her brothers. (TOS: "Mudd's Women")
The Omicron colony was an agricultural colony on the planet Omicron Ceti III. In 2267, Captain James T. Kirk noted in his captain's log that locating survivors of Berthold ray exposure there was most unexpected. Later, DeSalle mentioned in his biology report 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")
In 2268, Beta XII-A was a planet with a Human agricultural colony of a hundred persons. (TOS: "Day of the Dove")
Gault was a colony that was widely regarded as a "farm-world". (TNG: "Heart of Glory")
Coltar IV was the location of a farming colony in 2364. (TNG: "We'll Always Have Paris")