You can either move the LR from your old tank into the new one or start it from scratch. I wouldn't recommend using the old sand, just a mess either way. When I moved my 36 into my 55, which I did last night, I used one of the styrofoam containers that livestock gets shipped in. I filled it from water from the tank and straight moved my corals across the room in it. If i transfer my fish, it'll be by a similar process and my inverts will be also be transported by one of my styrofoam boxes, but the one that I use to drip acclimate.
For moving the LR over, make sure you have the livestock out before you move over any LR that is buried in the sand. Disrupting the sandbed can release nasty things into the water. This isn't just a deep sandbed thing, large amounts of detrius buildup around these rocks/sand can do nasty things if released into the water column.