Advice on a suitable climber

The rear of my house faces East and I'm considering adding a climber such as clematis or honeysuckle to a small section of wall. I would fix a trellis for it to climb.

My concern is as its east facing and I have a thick garden hedge plus a tree close to the area I'm considering planting, it will not get enough sun. 

Is there a climber that may be suitable, one which grows well without lots of sunlight?