Evening all, Conifer hedge help needed.

I don't think the hedge is Leylandii the foliage doesn't look soft enough to me.

 

To fill the hedge gap I'd be looking to see if any of the low branches on the healthy part of the hedge either side can be pulled down and tied at the same level as the bottom of the rest of the hedge. It'll look a bit messy initially but they'll grow into the space and fill it, exactly matching what's already there. The other option would be to cut that section out completely and replant, but there's a good chance the colour won't be an exact match and it'll take a while to fill in.

The other dead looking thing in the hedge is probably an ash or sycamore tree sapling. If the photo was taken when it was dormant it will have dropped its leaves the same as mature trees do. Cut it off at ground level and if you use chemicals in the garden, pop a bit of stump killer on it. If you prefer to avoid chemicals it will almost certainly come back unless it's dead, but if you keep removing the buds of new growth as soon as they emerge it will die eventually.