You can do it with or without expressions.
Without expressions can be a bit less intimidating if you don’t have any experience with them, but way less flexible to update.
In that case, do not parent it. Just copy the position keyframes from the original layer, paste them to the second layer and them select all keyframes (clicking the property name will do that for you) and move them to the right a bit. That will make the second layer do the same thing but with a short delay (which you can adjust by moving all keyframes a bit to the left or right).
The problem, of course, is: should you update the original layer’s position, the second layer will not react to match the changes. You would have to do all of this again.
With expressions, you could link the position of the “follower” layer to the main one using a time-based expression.
Alt-Click (win) or Option-Click (Mac) the position property’s stop watch and add this:
thisComp.layer(“OriginalLayerName”).transform.position.valueAtTime(time-delay);
“OriginalLayerName” of course is the name of the original layer. The one you want to follow.
time = current time. Don’t change it.
delay is a number in seconds (0.5 would be half a second, for example).
So, time-0.5 would means the original layer’s position half a second before current time. You can easily update it altering “delay” so it’s longer or shorter.
If you also want it for rotation, scale, etc do the same thing for those properties.
Adolfo Rozenfeld · Adobe