Are the posts wood or concrete? I just had to cut back the climbers because the weight was pushing the fence over and the posts had split at the bottom. They had to be repaired. It was my fence but the neighbour always shared the cost.
Please do not spend it on tall trees. They are a nightmare to control. They are very expensive to keep in check, and you would have to plant them a few feet away from the fence, as the branches will push into it. I know to my cost. I can put pics on here of my neighbour's trees.
If you can possibly afford it, buy arches and put them in front of the fence. You can grow climbing plants like clematis and roses - wysteria, beautiful climbing plants, honeysuckle, so many and some are evergreen. They will grow up the arches easily, and you can control them away from the fence if you want to so that the weight doesn't damage the fence.
It may seem expensive, but try it. The more you pay for an arch, the longer lasting it is. Agriframes last forever, but some of the cheaper ones are good too. Make sure you visit a centre where they have a good selection and you can buy an arch which supports whatever you decide to grow up it.
It will cost at least one arch for each panel. If you do decide to do this - actually it applies to anything you grow, have the builder cut piping - central heating piping will do, and put a length with all the plants you plant. When it is dry, you just put water into the pipe and it goes straight to the roots and doesn't dry in the sun on the surface.