Looks like aphids to me but I don't know how to treat it. Someone here will know.

If its aphids they can be controlled to some extent with insecticidal spray but there is a distinct danger that the brown parches will not recover. This is one of the recent infestations that are new to this country.

Or there is a possibility that the hedge was trimmed too closely. In either case if a branch has really died it does not green up again although the dead bits can often be disguised by allowing the green parts to grow up over them. You may have to wait until the next growing season to see if this will happen.