There are a number of climbers that originate from woodland areas that will be happy growing in part shade or fully shady conditions. You could try Hydrangea petiolaris which produces large heads of small white flowers in the summer. For foliage cover you could grow Parthenocissus henryana (Virginia Creeper) which has lovely bright red autumn colour. Sweet smelling honeysuckle is a fantastic plant to grow in the shade, particularly if you choose the evergreen Lonicera japonica Halliana (Japanese Honeysuckle) as you will also have winter foliage. Pyracantha will do well in a sunless position and will provide both summer flowers and colourful autumn berries although bear in mind it does have thorns. A slightly more unusual climber is Berberidopsis corallina which has lovely red flowers in the summer and early autumn.