No. You shouldn't have to remove the old insulation unless there is water damage or lots of mouse leavings or such.
Also, nice photo.
No, don't remove it. If it was me, I'd blow in more on top, or get unfaced insulation and lay it across the ceiling joist. Either way, wear a resperator for this job.
Unless it is somehow "gone bad" such as mold or critter remains, you can just go over the top of the old stuff.
Thanks to all. My pending project will now get started. Thanks for recognizing the photo of Gabby Hayes. Childhood hero who fought bad guys!
No...just supplement it with more blown-in and realize that it will settle over time and you'll need to add to it again somewhere down the road.
do not remove it, just add more