There are evergreen climbing clematis, evergreen honeysuckles.
Try Climbing Plants Direct, lots of climbing plants on there to give you idears,
Good Luck

A winter Jasmine (Jasminum nudiflorum) or an evergreen Jasmine (Trachleospermum jasminoides) would also fit your criteria. I have a few evergreen Jasmines in my garden (south facing, relatively dry). It has white flowers, winter Jasmine produced yellowish ones.

The summer flowering one would be easier to train up an arch though - the winter one likes to spread itself a bit.

Many thanks for your advice. Much appreciated.