So you have a bunch of clips all separated out by blank spaces between them and you want to delete all the gaps. With an easy change to your Keyboard Shortcuts in Adobe Premiere
First off open your keyboard shortcuts under the Premiere Pro CC dropdown menu.
Second, go to the search bar and type in “gap” to find the “Close Gap” and add a keyboard shortcut to it. I selected “Shift+Delete” for mine. Then click the OK button to save your shortcut.
Finally head over to your sequence timeline that has all those annoying gaps and hit the “Shift+Delete” keys and PRESTO! the gaps are gone.