Hi henry, As smurf says give a good watering as it might stem from the dry summer we had. Other than that there is a viris which can attack leylandii which starts off with brown patches but gradually moves through the hedge. If it is that, I' m afraid there is little you can do about it. But dont panic yet, it is a case of giving it time .Wait until the new seasons growth starts and take it from there. Cheers skylight
One thing to note with leylandii and similar trees, once there is no green left on a branch, that is it, it will never get green on it again. Worth remembering when trimming!!
Mine did that last year and it has died back but only in the middle. It is still putting out growth on the top so I don't know what's going on. I think someone told me it was some sort of insect that gets into the foliage.