Why are the leaves on my Clematis turning yellow?
If you are sure that your clematis is getting enough water, then this sounds like a classic case of magnesium deficiency. Some tomato fertilizers contain magnesium since tomatoes also need this trace element. If you cannot find a tomato fertilizer containing magnesium, which in general can also be an excellent choice for fertilizing clematis, an epsom salt solution is an alternative magnesium supplement.
While it is impossible to make a general 'prescription' that will fit all cases because it is impossible to diagnose the exact deficiency without a full soil test, you can try the following recommendation. Mix one teaspoon of epsom salt to one gallon of water. The mix can be applied in quart amounts at the base of the plant over a period of time until the yellow goes away. You should see fast results. Keep any left over solution for future applications, if necessary. Above all, use your own judgement on how the plant responds.