Thanks for the input. What about growing the hedge so that it grows through the the wrought iron? So 18 inches of the hedge would be in front of the fence and it would grow up through the fence and maybe extend another foot or so behind the fence? Is that something that is commonly done?

Also, What are good vines to use in LA that would have dense foliage? I've seen some on concrete walls that are thick enough that they look like shrubs before closer inspection. Anyone know what those are?

perhaps equisetum, plant in a raised planter if you need more height:

Why do you not want the hedge to be inside the fence?

If you want privacy oh, could you construct a more solid fence? And you could do away with the Hedge completely. It seems half the beauty of a wrought iron fence is the fence itself so it seems a shame to completely cover it from either aspect. Perhaps growing a Vine or roses on it that would still allow a glimpse inside

It is common for people to use sizeable plants (30'-40') "trees" in order to make large hedges. These large plants achieve the hedge quickly and, other than a lot of trimming over the years to keep them in bounds, serve the purpose reasonably well. But the short hedge should not use this strategy. Instead, In this short range, pick a plant that might have an appropriate finite height built. Liriope comes to mind as it many of them get into the 18" to 24" height range. And, it's a adurable, evergreen plant. Instead of trimming, it needs a knock-down every year or two and it quickly resumes its position with all freshe foliage. Some of them have nice, unobtrusive blooms for 3 or 4 weeks during the summer.

A common vine covering for walls in warmer climates is Ficus pumila. It might be what you're asking about. Often, it is clipped in the shape of the wall, so almost looks like acrips architectural wall made of green, leafy material. It is fine to have it this way and just keep trimming it as a hedge. However, if you take a trimming break, the hedge will break into an adult growth stage, producing outreaching "arms" of foliage that extend 5' or so from the hedge portion. These can all be cut off, returning the plant to its former hedge state, but it is a lot of work, so best not to let happen. If not cut off, the whole plant will turn into jungle monster.

Back to the initial question, there are probably all kinds of groundcovers/perennials of the height range you are looking for that could be used, liriope being just one. But most of them would need to be cut to the ground annually and regrow fresh. If you wanted something flowering, you could use 'Stella d'Oro'' dayliliy, or something like that (if it grows there.)

Here Lirope wouldn't provide any privacy. I may have read incorrectly, but I interpreted their post to mean they wanted the depth to be 18". I didn't read a height requirement, but am assuming somewhere in the 5'-6' range.

I can't think of anything that will provide privacy and stay 18" deep over the long term. I live in an older neighborhood where too many people have planted along a front yard fence line and the plants now block the sidewalk. I think you have a couple of alternative options. One, place the fence farther back on your property and plant tall, skinny shrubs that will survive in your region (Google fastigate or columnar shrubs). Two, plant your privacy screen in your front garden and edge the outside of the fence with some hardy low-growing plants. Good luck with your project.

Depending on the height of the fence you might be able to achieve partial obstruction with espaliered planting, but there is upkeep and proper initial establishment. I sense it's more than you're looking to do. Many good suggestions here.

If the depth is 18", then the realistic height max is probably 24" and that's pushing it.

Stephen -- Had a thought while out walking the dog. A dwarf Italian Cypress might work, providing they're appropriate for you area. You'd need a lot of them to get coverage and they're fairly expensive but it could be an option.