I can't really make out what species the hedge is made up of, but I'm sure it is a conifer, possibly x Cuprocyparis leylandii or similar. It looks like it has been cut back too far - it won't recover, I'm afraid. Hope I'm wrong, it looks very large!

It looks like ours after an odd jobbing "gardener" cut it back too hard. But there's also a disease that does this to them. either way its unlikely to green up again. My solution is to plant an evergreen shrub in front of the bare patches.

I think it can depend on why it went brown. If its cut back too far or suffering from the new disease then it won't. But one near us suffered bad wind burn one year and did recover.

From my expirience it looks like damage caused by the conifer aphid, large patchy brown areas are a tell tale sign but if you look further into the hedge aprox 4/5 inches then you will notice sooty mould this is a sure giveaway that it's the confer aphid, it looks like the hedge is leylandii and rest assured the brown areas will not come back, spraying with the appropriate bug spray aprox three times a year will keep the hedge free from aphids, the damage is mainly caused through late winter early spring but only noticed in early summer by which time can be too late.