Make a high wall higher with climber?

Hi EssKay, welcome!

Lonicera Henryi is evergreen, vigorous and has lovely flowers. It would easily grow from the ground to the 4m or so you need, if you can fix a sturdy trellis to the wall. It tends to grow heavier on the top so the lower part of the wall could become bare over time.

I bought mine as a tiny 10cm plantlet from Morrisons and it grew to the extension roof (and gutters) in one summer even though it was in a container.

A very nice plant for practically instant greenness