To do that, hold down the Grave Accent (`) key and drag the clip to another location in the timeline using Select or Position tool. It also work with the Trim tool which is my favorite. Hold (`) and drag the clip with the Trim tool will modify its start/end point without moving any connected clips. FANTASTIC! Try it! It'll save you loads of time.
And open the submenu: Edit clips in the primary storyline without affecting connected clips.