Experts and BHG readers answer.
evergreen vine to cover a section on fence
"The small-leaved climbing fig (Ficus pumila) will attach itself to whatever it is growing on with small sticky pads, making a dense cover. Since you want a vine that will clamber over the fence, leaving some air circulation beneath the growth, consider these vines:
Cross Vine (Bignonia capreolata), semideciduous, orangy-red trumpet-shaped flowers, medium-sized compound leaves, climbs with tendrils, best in moist, organic soil
Spanish Jasmine (Jasminum grandiflorum), evergreen compound leaves, clusters of white flowers, moist soil, flowers best in full sun, but will bloom with some shade
Mandevilla (Mandevilla x amablis), fragrant pink trumpet-shaped flowers, glossy evergreen leaves, moist organic soil, may be it bit shy on bloom since it does prefer full sun
Confederate Jasmine (Trachleospermum jasminoides), evergreen vine with small leaves, fragent white flowers, partial sun, moist organic soil, will need trellis or other means to climb the fence, slow-growing