What are the plants in the hedge? We can't tell from this distance. Can you post a close up of leaves/buds and bark? Best guess at present is privet. There is one plant in the middle which is something different. There also appears to be a shrub behind the hedge on the left which may be partly responsible for it leaning forward like that.

It looks as if the hedge has been cut high repeatedly. This means you get a lot of twiggy growth at the top and no new stems from the ground. If you cut out a proportion of the stems right to the ground it should start to throw up new shoots from the base. I don't think you need any new plants. Just some rejuvenation of the existing ones.

I agree that it is probably privet. However, it also looks like some trees have been allowed to grow in it. This is a problem with shrubs that haven't been carefully kept weeded.

What I would do is cut the whole thing down to about a foot. Identify the trees, cut them shorter, and paint straight Round Up on the stumps to try and kill them. The privet will grow back quickly, and the hedge can be shaped properly.

Yes, cutting the whole lot down would certainly work fine. I was just thinking of a way to do it gradually so the hedge effect remained visually whilst it regenerated. The tree will be easily identifiable when it leafs out although it is already pretty clear which plant it is from the trunks and bark.

google: rejuvenation pruning of flowering shrubs.. and learn how these should have been maintained over the years ...

i cant focus on the pic... are they greening??.. is there any green growth down low??

if so.. i would cut the lot to 3 to 6 inches.. do maintenance on the porch behind..

and with no insult to the root mass .. they will probably be half as tall by fall as before ...

BUT!!! .. your problem is not the lost shrubs ... the problem is that you have a 3 to 4 foot wide shrub in what looks like a 2 foot garden bed ... if it were me.. they would be removed.. and some short perennials would be planted.. that suited the site better ... say something in the 2 foot range ... so as to show off the decorative bottom of the porch.. and then i would contemplate some type of vines to grow up the porch.. such as morning glory for an annual.. or a clematis or two for perennials .. this is the front of your castle.. it is screaming out for a drop dead solution.. not maintenance of a problem ...

might you be up for that struggle???

ken