Star Trek: The Motion Picture (Vectrex)

From Memory Alpha, the free Star Trek reference

Star Trek: The Motion Picture was one of the first games created for the Vectrex Arcade System, a self-contained vector graphics home gaming system. The system included its own game screen (which required plastic overlays to simulate color graphics) and a controller with 360-degree joystick and four control buttons.

The object of this game--a basic "shoot-'em-up" style game for 1 or 2 players--was to travel through space and destroy Klingon and Romulan ships. Gameplay had you flying the USS Enterprise through nine space sectors trying to reach the "Klingon Mothership" in Sector 9. Players could control shields and phasers and dock with Space stations to refuel.

NOTE: This game is not a port of Sega's Star Trek: Strategic Operations Simulator arcade game, which came out around the same time. That game would be translated for game systems of the time much later.