I think a retaining wall is needed wall behind those trees. The rest you probably just need to keep mulched.

The dirt will wash down during rain unless you plant the area to grow solid with a groundcover and mulch it. You will need to give it regular inspection and possibly occasional repair attention until the growth begins to become solid.

Hi Sue, I like your trees. What are they called?

Skyrocket junipers

The gap under the neighbor's fence is only going to get worse because you cut into and disturbed the slope on your side. It will continue to erode until the slope returns itself to a smoother angle of repose. You can fix that now with some fill dirt and regrading of the slope.

Painting the bottom of the fence would help matters too.

Why do all your plants look like they are planted while still in their pots? Or is that plastic edging of some sort and what is its purpose? To keep the drip water in?

Yes it's just a liner to keep the drip water from going down the slope. The fence was like that when we purchased the house. I can't fill in more dirt, it will slide right down. I think I need to plant some plants to keep it from eroding more.