Vader and Bast
Immediately after the Jabba scene is another scene cut from the film: Darth Vader talking to an imperial officer (now canonically named Moradmin Bast) regarding efforts to retrieve the stolen Death Star plans. Bast informs Vader that they are now searching Mos Eisley for the droids, and they will capture the droids soon. Vader tells Bast to send more men if he has to, as Princess Leia’s hope that the Death Star plans being used against the Empire is the “pillar of her resistance to the mind probe.” Bast replies that, until then, they will have to “waste ou[r] time with Governor Tarkin’s foolish plan to break her.”
Why it was cut
Editor Hirsch said this short scene was dropped because it serves little purpose in the film and tells the audience what they already know: the Empire is looking for the droids. Additionally, like the Jabba scene, this scene adds additional runtime before the heroes leave Tatooine, which Lucas and his editors continuously tried to shorten. The only significant addition of this scene is giving more explanation for how Leia was able to resist the mind probe, but audiences can largely infer this.
Footage from this scene was later dubbed with new dialogue and included in the infamous Star Wars Holiday Special in 1978.
 J. W. Rinzler, The Making of Star Wars (New York: Del Rey Books, 2007), 258.