It's probably an aphid attack which thrive on well trimmed Laylandii. Regular spraying will help but it usually spreads to unaffected parts. About 6 years ago I gave up and planted a Yew alongside so soon I will cut down the Leylandii.

There's alot of this about this year. As Heron says it is priobably an aphid attack but if the leaves are brown nothing you can do will bring the green leaves back.