Adobe Premiere crop one side - then fill the frame -
To crop just one side of a clip, select the clip in the timeline and open the Effects panel. Search for 'crop' (in the current version of Premiere Pro, the effect can be found under Video Effects → Transform). Double-click the effect with that name to apply it to your clip. Then open the Effect Controls panel, there you will find the effect settings for the crop effect with allow you to specify a crop amount in percent for each side.

To have the cropped image fill the frame, use the effect controls of the Motion effect that is applied to all clips in the timeline by default. Use the Position and Scale controls to adjust the clip's position and size to your liking.