Trimming to the boundary of the next clip on the timeline should be easy, and it is. The necessary commands are found under the edit menu. See the comments on the images in the slideshow to see the options.
The green Clip needs trimming to fill the gap in the red clip.
Using Edit - Trim Start To Fill Selection extends the green clip to the beginning of the edit selection.
Using Edit - Trim Start To Fill Selection extends the green clip to the beginning of the edit selection. As we see here.
Using Edit - Trim End To Fill Selection extends the green clip to the end of the edit selection.
Using Edit - Trim End To Fill Selection extends the green clip to the end of the edit selection. As we see here.
Using Edit - Trim To Fill Selection extends the green clip to the beginning and end of the of the edit selection.
Using Edit - Trim To Fill Selection extends the green clip to the beginning and end of the of the edit selection.