Place the scrubber (red-line) where you want the new content dropped in. To locate the precise split point between clips use the buttons under the preview window or shortcut keys.
In the bin, right-click the new clip and PLACE ON SEQUENCE AT CURSOR.
Another approach....
Select all clips to the right of where the new one is to be added, then drag them to the right. Don't press <ctrl>. If they snap back, hold down <alt> while dragging. Drop the new clip into the gap that is created. If there's a gap left over, right-click in it and CLOSE GAP,
To select all those clips, click on the first one, hold down <ctrl> and click on the last. All clips in that range will be highlighted.