We might get a better idea of what's causing the damage from a view of the entire afflicted plants, but it could be disease (particularly one of the canker fungi for the leyland), root stress, or a wood-boring insect (for the arborvitae). All you can do is to prune out the completely-brown foliage or dead branches with no green growth on their tips. There are no pesticides recommended because they will not provide any benefit, nor can they reverse existing damage.

Both evergreens prefer soil that doesn't get too dry but also require the soil be very well drained. Neither has good tolerance for soggy conditions, whether that's from an influx of extra moisture (such as from a nearby roof downspout outlet or gulley), irrigation when it's not needed, or heavy rain that can't drain quickly through compacted soil. If irrigating during hot, rainless periods in summer or autumn, make sure the soil feels fairly dry to the touch several inches deep before watering.

Miri