The photo is on its side , what is the plant used to make the hedge?

Leyandii or similar. The gaps will not grow back and will only get larger. Apart from replacing the hedge(!) you could either fill the gap with short lengths of fencing to keep dogs etc out, or plant other shrubs in the lawn to block the view of the gaps.

Nice hedge. Am guessing it is Thuja? Filling in the spaces with cuttings or small plants of the same species might plug the gaps - would have to add in fertiliser and fresh compost and keep it watered for them to stand a chance of growing.