Hello Vicvic92,
This may not be everybody's favourite, but Mahonia x media or Mahonia japonica can grow tall and thin with slim stalks (beneath which you could plant something else) topped off with foliage and, in winter, fragrant flowers. I was thinking about bamboo, but planting even the 'non-invasive' types with a submerged barrier next to your fence could make you unpopular with your neighbours. There are also some lovely tall, slim cultivars of evergreen shrubs, like Ilex crenata 'Sky Pencil' that could do the trick, but they are pricey to plant en masse. Let us know how you get on,
Emma
gardenersworld.com team