How about a lavender hedge. Munstead is a nice compact one and is evergreen. Just needs a trim after flowering each year

There are several varieties of Euonymus that have attractive leaves and they're all evergreen.

As this border is less than 6 inches deep, you're very restricted as to what you can plant. Inverglen's suggestion of a lavender hedge is a good one if your border is in full sun - but use Munstead Dwarf. Otherwise, it'll have to be Euonymus microphyllus, or Buxus microphyllus, if you cannot widen the border. You can, though, put in some perennials such as Campanula persificolia, campanula muralis, Sisyrinchum Aunt May, anything that gets taller without being wide.