fast growing climbers?

Cobea scandens (cup and saucer) plant. This is a fast growing climber.
Morning glory.

Something more permenant Passion flower.
Hope this helps.

I love the passion flower. It grows quite quickly and has an abundance of beautiful blooms. There is a picture of one in my photos.

Lonicera similis delaveyi or clematis amandii both are evergreen. Since you want privacy that is ......

Yes, I've got passion flower out the front, & clematis armandii out the back for evergreen cover. I've got very dense jasmine mixing with solanum along one side fence, though these aren't evergreen - they give good cover for most months of the year (near London). We've also got a few types of bamboo for evergreen screening (not climbers, of course, but very effective), although we have to keep a close eye on them & thin them out hard. I've never fed or improved the soil for these, other than planting them with compost in the first place. Also, laurel is not a climber, but densely bushy evergreen, & ours are pretty big after 4 years from quite small plants that self seeded in my mum's garden.

There is the cirrhosa group of Clematis, too - evergreen and flowering very early in the year. C.cirrhosa 'Wisley Cream', C.c. 'Balearica', C.c. 'Freckles' and C.c, 'Jingle Bells'.You could add one of these alongside one of the other suggestions already made!

Nothing more beautiful in the Spring than Lady Banks Rose . It does not mildew or black spot , nor does it have any thorns. Just keep it in bounds as it loves to clamber!

Rambling Rector Rose its a fast climber its flowers are white

Clematis Montana is wonderful and grows really quickly, you are rewarded with a stunning display of masses of flowers in May which is so very enchanting.Hel.xxx.