Not quite sure how to answer this, not enough information really. You can cut off branches which are dead or dying.

Hello ... I have found that conifer hedges (especially leylandii) die back for 3 reasons - drought, cutting the sides too hard and an aphid/whitefly borne virus. Any conifer hedge under stress will succumb to the virus. If it is the virus then the only solution is to spray. You will need a decent 10 litre sprayer with the penetration power. Suggest you bash the hedge with broom or flat rake to dislodge ladybirds feeding on the bugs. If you are south of the border and weather still mild then do this asap, then again early spring and in the summer. It will stop virus spreading but won't kill it - just the bugs that cause it which will give the trees time to grow and replenish. It will be an on-going job three or four times a year until the hedge recovers! Also, don't trim the hedge back too hard - only trim the new growth lightly as it appears. If you have no new growth this year then I suggest it has been cut back too hard every year. You can top out a conifer hedge but not the sides.