Upon beam in, Elliott reported that the Constellation's radiation level was normal. Once the landing party split up, Elliott joined Scott, Russ and Washburn to main engineering to check and see if the ship's phaser banks had been fired.
While in engineering, the three ran a complete structural and control damage check while Scott checked out the ship's engines.
Later, when the Enterprise was attacked by the planet killer, the damage control party became stranded aboard the Constellation, when the Enterprise's transporters went down. In effort to assist the Constellation, Elliott assisted Scott in cross circuiting the warp drive controls with the impulse engines.
Once repairs to the Enterprise's transporters were complete, the three members of damage control party returned to their ship, while Scott and Kirk stayed behind to rig the Constellation for destruction within the planet killer. (TOS: "The Doomsday Machine")