Trim the top.
This usually will force out growth.
If plant does not get enough light, nothing will grow.
References :

If you cut the top the sides grow thicker, and cut the sides they grow taller. Cut weekly and the clippings should be swept under the hedge, to rot down and feed the trees, so any shoots growing in the gaps can be snipped shorter to encourage thicker growth. This process will take some time.
Best of luck
References :
Growing a shaped hedge

To rejuvenate an old and “leggy” hedge, cut back to a few inches above the ground in the early spring and then prune like a new planting. This works best with deciduous hedges but is also possible with some evergreen hedges if you leave a few branches with leaves on the plant.

. Larger, older shrubs should not be rejuvenated in late spring or summer. Early spring is preferred for most.
new growth can be pruned back to help keep shrubs the size and shape desired. With hedges such as privet, prune them so that the lower portions are wider than the upper, so all leaves get equal light. This will help prevent the lower portions from dying out. Avoid pruning the side perpendicular to the ground or angling in toward the base. Hedges in poor shape should be rejuvenated and the new growth then pruned properly.
References :
U. Illinois Extension Office

The way to keep it thick at the bottom is to prune and shear it properly. If the bottom is shaded it will become sparse and the main cause of shaded bottom is cutting it wider at the top and thinner at the bottom.

Start pruning your hedge in a wedge shape, wider at the bottom end and it will thicken up. See the link below for more details.
References :
http://ag.arizona.edu/pubs/garden/mg/pruning/hedges.html

I have a great privet hedge that many neighbors comment on.
Make sure that you avoid the tendency to trim the top wider than the base. Your verticle lines should be 90 degrees to the ground. I do my main trimming after the blossoms have mostly disappeared. In the winter, cut out about 1/3 of the oldest main branches at the ground. Fertilize your hedge with a balanced fertilizer. I prefer 12-12-12. Water in times of drought or if your hedge is young.

I wouldn’t do the 1/3 winter trimming thing untill the hedge has been in place 10-15 years.
References :

Most of the answers about leaving the bottom thicker than the top works, this way the bottom will get more light. Next time you are in a country road observe how the Council cuts the hedgerows and you will see the way to do it.
References :
Experience.

cut some lems back to the second joint and put them in water till they get roots then plant them in the bare spots as the hedges get to the height that you need you need to cut the tops off this will make them thicker and you will not even be about to see thought them anymore it will take some time to do this but it is what you want and this is the best way that I know how to do this without having someone to come in and planting a fence role hedge in it place even that would have to grow up to block the lookers
References :
working on a hedge myself