Firstly,Victoria,do you have any width restrictions ie,a narrow border,or do you have plenty of room,for spreading roots..? also ,would you need access ,either to paint or maintain your fence at some point? If no to either,have you thought of evergreen Pyracantha's ..flowers in late spring,to be followed by berries in Autumn..much loved by birds,I might add..Whatever you decide on,they would need to planted away from the fence,so as not to dry out ,in the rain shadow...or to remember they need watering well...like most things...Some varieties climb more than others,whilst some are bushier..but it will tell you which,on the label...hope this helps..I'm sure you will get many other suggestions..and welcome to GoY...

Have you put anything on the fence for the climbers to grow up and which climbers have you been trying to grow?

Hi, Hydrangea petiolaris is self clinging, and does well on a north facing wall or fence, and is a pretty fast grower, you should have no problem with it, Derek.

Could you tell us please what you tried that didn't grow?

Has the fence been creosoted? Creosote leaching into the ground won't help.
Do you want climbers for the plants themselves or to disguise the fence? If it's to disguise the fence there may be better options with coloured paint/preservative which will give quicker results.

I'd echo Steragram and Bloomer's questions specifically, and also ask how wide is the border in front of the fence?