Yes! That's a great idea. The real question is why the original rose died. Without knowing that we're just guessing. I'd always read we don't have Rose Replant Disease here in the States so there must be something else in the soil or drainage that's changed, causing the die-off as suggested above. If the rose died of gall, that could have infected the soil and remains active unless it's entirely removed. In that case, it's probably best to plant something else there and train the current rose to grow on that side.