Do you know what clematis it is? It may be one with a more compact growth habit that would be unlikely to grow over the top of the fence. The fact that it reaches the top of the fence yet does not grow out laterally from that point would seem to confirm that.

Regardless of the specifics, I would give it a hard prune this winter, taking it back to as far as you can. Somewhere around 12-18 inches. Apply a good dose of alfalfa meal and mulch well.

Construct your support system. Maybe just string a wire laterally a couple of inches above the top of the fence - easy to attach your fasteners to. You will have to train it vertically as it starts to grow, otherwise you might face the same forward sprawl again next season. But no guarantees the clem will grow tall enough to spill over the top. Just might not be in its genetics to get that big.

Thanks Gardengal. I forgot to mention I had prunned it last winter not to 12-18 inches but more close to 36-48 inches, but I did not string tie the new growth this spring. Crawling on the ground is a new behaviour this year. However, prior to this year, it would grow to few inches above the fence and then stop there or weep backwards not forward. Unfortunately I do not remember the names , there 2 of them, one of them Group B and other Group C. One of the could be type President, I am vaguely recollecting.

Finally this year, the clematis has grown over the fence. The changes I had done earlier this winter were 1) Put a small metal mesh just at the top of the fence wrapping over the fence. 2) Did not prune the clematis at all in winter as I usually do, as a result no new growth around middle and bottom of the fence but lots of growth in the upper section of fence.

Now I am not not sure if I should refrain from pruning again this year.

In photo 1, how the bottom half no new growth. All growth in the top half this spring.

Photo below, how nicely it has grown over the fence and also visible the additional metal mesh added earlier.