I have a similar problem at the bottom of my garden since we reclaimed a bit of land next to the summerhouse. I've been researching this and found the following advice from the RHS. It is from
They say that (among others) the following plants are good for shade.
'Clematis alpina, C. macropetala, C. montana, C. Jackmanii Group: Deciduous; flowers variable according to species or cultivar; 2-7m (6-22ft)
Lonicera japonica ‘Halliana’ AGM or L. periclymenum cultivars (honeysuckle): Semi-evergreen or deciduous; flowers, sometimes fragrant, from spring to late summer in white, yellow or pinky-red; 10m (30ft)'
Obvously, one would have to choose the smaller among these, or be prepared to do some hard pruning. Type of soil is also an issue.
In general, clematis (as you probably knkow) like their feet in shade and their tops in sun, and some actually fade in sunlight, so there are others not mentioned in this list that would be good. I have foiund, though, that you don't get much of a display on an arch unless you put in more than one of the less rampant clematis.