Unfortunately, you should not expect to see strong new growth from these clipped mature branches. When newer growth on a branch (just one year growth at the branch ends) is pruned, it can regrow from dormant buds. For that reason, starting a pruning process when the plant is young and maintaining it annually (so you are always cutting into newer growth) can keep an arborvitae from growing into a neighbor's or the municipality's right-of-way. In late winter or early spring, cut branches back young branches to a side branch (lateral) and do not cut back more than ⅓ of the total length of the branch. This type of pruning will produce a fuller and more compact habit on healthy trees. 

Once an arborvitae tree branch is mature it does not generate new growth when it is clipped back significantly. You should see some additional green growth initiating in spring, particularly from branches where cutting only reached back into one year's new growth. That will help to mitigate the overall impact on the hedge's appearance, but your trees will not return to the uniform, dense green form you had before.

Courtesy of NYBG Plant Information Service