eucalyptus

A tall fence with Russian Vine on it.

I wonder if they took out the roots? If not the ......maybe you don't need to worry about what to plant. Give it a good feed down there, lots of rain you might have been having, and it might be back quite smartly. Maybe your shrubs, whatever they are, will grow more too, with the feeding, now the laurel has gone? If you want to spend a bit more........ lash some bamboo screening onto your fence as well.....then the trampoliners will have privacy for their exploits. Old folks are often badly sighted, don't use their grounds that much, and probably don't like looking at you either, after the chainsaw massacre.

In your first pic it looks to me as if the Laurel was behind their/your Hedge? If so let this hedge grow and help it with a good feed. The laurel will grow back fairly quickly too.If you plant a tree about 10-15 ft from the boundary the perspective will
give you quick cover when looking from where you took the pic. You already have one on the left of the pic that gives good cover.

Plant your own laurel (Prunus laurocerasus) on your side.