I start by going up and checking the whole attic, edges included, for wet spots, stains, droppings and insulation packed flat, because that tells us what has to go and what doesn't. We only pull old insulation when it's wet, fouled by pests or too flattened to do its job, and otherwise I'll tell you it can stay. When something has to come out, we cover the path through your house, take the old material out and clean the attic floor down to the framing, so the new layer isn't sitting on the old problem. A roof leak or the gap the pests came through has to be fixed before anything new goes in, or the trouble just comes back under fresh insulation. Then we air seal, closing the gaps around can lights, pipes and the attic hatch, and insulate with the eave vents kept open and the edges as deep as the middle. If anything up there looks like vermiculite, we stop right there and point you to a licensed abatement firm, for the reasons in the questions below.
The same problems turn up in other parts of the house. Wet or fallen batts under the floor come out and get replaced as part of our crawl space insulation work, and when a wall has been opened after a leak, the soaked insulation inside comes out before we do the wall insulation.
Leave it and top it up
If the old layer is dry, clean and still fairly full, it stays, and we seal the gaps and add blown-in, loose fill blown through a hose, right on top. It's usually the least you'll spend, and it's the answer more often than people expect.
Pull the damaged section, keep the rest
This suits an attic where the damage stays around one leak, one nest or one corner the pests used. We take out that area and a margin around it, then build the new insulation back up to match the depth of what's left.
Take it all out and start clean
This suits an attic where the whole layer is wet, fouled or flattened, or where you're changing to a different kind of insulation. It costs more up front, but it's the one way to see and seal every gap before the new layer goes in.