Right. It's in the Drag and Drop Options.
By default, a dialog box opens when you move a clip, but you may have turned that off.
If you don't see the box, right click on the clip, scroll down to the >>> at the bottom of the list, and select Drag and Drop Options.
Make sure Slide Over Old to Make Room is not selected.
If you select either the Blend or Replace option, the old clip does not move.
You may want to turn on track layers to get a better view of where your clips are, instead of having them stacked up.