Can you be more specific in your location?? Zone 7 covers a lot of real estate :-) What is the fence constructed of? If you don't want any dead leaves, does that mean you prefer an evergreen vine? Flowering?

Unfortunately, plants provide minimal sound deterrence unless they are very densely and thickly planted (like a 100' depth of solid plantings) - your fence/wall is providing you with as much of a sound barrier as you are likely to realize.

We live in Nashville. The fence is a wire fence. Not chain link, larger squares. What do you suggest?

Acknowledging that vines will not provide much of anything in the way of sound deterrence, you are not exactly limited in what you choose. Clematis and honeysuckle are two of the most commonly planted ornamental perennial vines but you could also consider trumpet vine or even a wisteria if the fence a strong enough support. Grapes would provide good coverage as well in lots of sun and there are ornamental as well as fruiting varieties. Or Akebia (chocolate vine) or kiwi (Actinidia species).
Vines common to Tennessee and the southeast.