What version of Premiere Elements and on what computer operating system is it running?
Generalizing....select all the clips that you want to move as one, and, with the mouse cursor, click and drag anywhere in the selection to close the gap.
Is Delete and Close Gap not working for you in what you are doing?
To select all the clips (altogether) that are going into the selection (group) to be moved, hold down the Shift key (Windows) and click each of the clips going into the selection.
You can also select a group of Timeline clips by drawing a rectangle around them with the mouse cursor.
If you want a more than temporary selection for the grouping, select all the clip and then go to Clip Menu/Group.
Please review, consider, and supply more details for a more customized reply.