A ground assignment was a posting on the surface of a planet, as opposed to a starship.

In 2267, after citing Captain James T. Kirk's apparent culpability in the death of Benjamin Finney, Commodore Stone offered him an ultimatum – either accept a permanent ground assignment, or face Starfleet Command's discipline. Kirk chose to fight the charges in a court martial. Later, after initially calling Kirk a murderer, Jame Finney apologized for her grief-induced outburst and begged Kirk's lawyer, Samuel T. Cogley, to make Kirk change his plea and take a ground assignment instead, as she no longer blamed Kirk for her father's death. (TOS: "Court Martial")

In the Pocket TOS novel The Captain's Oath, Kirk takes a temporary ground assignment near his ship, the USS Sacajawea (β), while it's being repaired, so that he can remain near the ship and his convalescing crew.
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