It might be being shaded out by the conifer next to it. I would cut it down to the ground, then see if it regrows - they usually do. If the conifer belongs to your neighbour, you could agree to cut it back to the boundary line to allow more light in.

Is it another conifer that has died, or another laurel? If it's a conifer, they do just die off suddenly and just will need to be replaced. If it is the laurel, cutting it down with stimulate new growth, but not if it is a confer as they don't usually regrow.