Do you know the variety? If it isn't a Montana or other clematis that only blooms on old wood it can be pruned. Is it blooming now or budding?

Pruning two clematis are usually early bloomers and large flowered. If it is a prune three clematis then it does best if pruned close to the ground every year. Those not pruned often end up as you described with blooms only at the top.

Most of my early blooming prune 2 clematis die back to the ground in the winter. The bloom is later and those that are double with first bloom may have few on no doubles, blooming single instead. Still get a nice full bloom in the spring with sporadic blooms until frost. In my zone I do not get a full bloom in the fall as there isn't enough time for regrowth to get another bloom.

Sounds like an old plant. How thick are the stems? That may make a difference on how far to cut back.

Hard pruning a clematis will seldom do it any significant damage and almost always helps. I would avoid cutting back to the ground - that's a bit too severe - but if the stems are pencil sized or smaller, cut back to the third set of buds or paired leaf axils (or where leaves were before they dried up and fell off). If the stems are larger in diameter, be a little more conservative and leave more..

When you do this is flexible. When does the clematis bloom? If it has already bloomed, you can do it now. Or you can wait until fall or late winter. If you do it now, you can go ahead and fertilize after hard pruning. I prefer an organic rose fertilizer as those typically container alfalfa meal which encourages additional basal stem growth. If you cut back hard in fall, skip any fertilizing until spring. A late winter/early spring pruning can also be fertilized at that time.

Most types of clematis benefit from annual pruning or at least those in pruning groups 2 and 3, with flowering beginning May or later. This will prevent that bare/dead leggy look with flowers only at the top of the vine. If it blooms very early, like before that start of May, come back and let us know. Pruning of these types of clematis is quite a bit of a different process.