Shrubs in Partial Shade

3 to 4 hours sun in the summer is really pretty shaded, so you will be a bit limited. Most screening shrubs are not big on flowers, but you could try rhodos that grow large if you have the right soil.

I have a similar border where I grow evergreen shrubs as a screen from my neighbour and for my chickens to scratch about under.  Mixing different foliage shrubs together can give a nice effect.

My selection is :

Aucuba japonia - yellow speckled green leaves
Pittosporum - available as green leaved and also variegated leaves
Fatsia japonica - green leaved
Bay - this is the basic cooking bay leaf, but it is surprisingly shade tolerant
Chiosya Aztec Pearl - this is the only really flowery one of the bunch
Nandina domestica - has brightly coloured new leaves and also changes in autumn as the cold hits it

You could also try Photinia Red Robin, which does have white flowers in the spring, but every new leaf comes through bright red and this is an attractive contrast against the green older leaves.

Hope that gives you some ideas 

 

Two excellent shrubs for the conditions you require:- Berberis Darwinii, and Viburnum Tinus. The Berberis is a little faster growing, and makes a looser hedge,  but is prickly. Both will reach 6' or more within 4-5 years and flower profusely in spring, but the Viburnum begins flowering in late winter.

Euonymus in its variegated forms such as Green and Gold or the green and white one can, if planted against a fence, grow upwards quite easily and is evergreen. They are easily cut back to whatever height, depth and width you require. It does have flowers that are in small clusters that look like a tiny cauliflower.