I'm not sure if it works in Elements, but in Premiere Pro you can select the new clip in the Media panel, right click on the old clip in the timeline, and choose Replace clip > From bin.
You can also right click on the old clip > copy. Then place the new clip on the timeline with the same duration, right click, and choose Paste Attributes.
What version of Premiere Elements and on what computer operating system is it running?
From the Premiere Elements rather than the Premiere Pro perspective...
Generalizing for now....with Premiere Elements 11, 12/12.l, and 13/13.1 in mind....
In Project Assets, right click the thumbnail representing your Timeline video and select Replace Footage from.
The major attribute of the Replace Footage feature is supposed to be replacement without loss of the edits to the file being replaced, but there
are limitations - just some expamples
a. you cannot replace a video with a still or a still with a video
b. if the duration of the original and the replacement are different - problems
But worth checking out for your purposes and your specific clip attributes
Although not without its own limitations, probably with more applicability,
a. video or still with edits/effects etc....right click, select Copy
b. select all the other clips (still or video) and then right click anywhere in the selection
and select and click on Paste Effects and Adjustments.
Some attributes of the clip may not copy/paste.
Also see creating effects presets for the fx Effects/Presets.
Possibility....apply multiple effects to a clip to create a special overall effect....go to Applied Effects Tab/Applied Effects Palette/ and find the Panels for the
fx Effects applied (including a Motion Panel for example if scaling. Select all the panels involved, right click any one of the panels selected, select Save Preset.
The saved preset will be available for use under fx Effects/My Presets to give you special overall effect when applied to another clip.
Just some Premiere Elements thoughts for you to consider.
As your schedule permits, please let us know of your progress.