Get a taller fence. Or plant ornamental grasses, maybe. Exactly how wide is that teeny tiny strip of grass? Is it at least a foot wide?

If you are up for some ongoing maintenance you could pleach trees that lend themselves to training/espalier. Apple, pear, plane tree, camellia, some hollies.

Just be aware you are signing up to prune and tie in at least once probably twice a year to keep it looking good.

Or get a taller fence.

Preached trees-

https://www.google.com/search?q=pleached+trees&rlz=1CDGOYI_enUS590US590&oq=plea+hed+&aqs=chrome.1.69i57j0l3.2753j1j4&hl=en-US&sourceid=chrome-mobile&ie=UTF-8

The whole point of a tree for privacy would be that it is full at the lower part and IMO you do not have room to grow a tree od any size there unless you cut away some patio.I don’t think you can grow anything in that tiny strip of dirt since it looks like a sidwalk outside the fence and the patio next to the strip of dirt. Is this your driveaway ? Maybe take a couple more pics of the house and driveway .

The whole point of a tree for privacy would be that it is full at that portion of the tree that provides the maximum screening for your purposes. Since the OP already has a fence that provides adequate screening at the lower level, you want a tree that provides the majority of its screening features above the fenceline.

Street trees are often planted in very tiny openings in the middle of a concrete ground plane so it can be done. And a pleached screen is an excellent idea although well beyond the maintenance desires (and skill level) of most homeowners.

I don't know what zone you are in, but I wonder if a vine, like evergreen clematis would work better than a tree? With training and proper trellising, it can cover a lot of area.
I would be cautious about wisteria, though. I see a trike in the pic. Wisteria is quite toxic if ingested.

About pleaching ... you will need access to both sides of the trees. Are the neighbours amenable?

Thank you for all your recommendations. We have about 30 inches to plant something.

were leaning towards arborvitae due to the low maintenance aspect of it.

Does water drain off the paving into that lower level occupied by the bed? Because if there is ever much puddling there the 'Smaragd' arborvitae most people buy these days is more prone to root rot than usual for Thuja occidentalis.

Also even with that compact and narrow growing selection the time will come some day when it is starting to bulge over the pavement and eat the fence (if it grows well in that strip). You could shear them but this can't be done back to the same point indefinitely because the surface of the hedge will start to turn to mostly bare stubble. And if you choose any kind of conical conifer (including arborvitae) it has the wrong shape for your situation, because most of the width is in the lower half of the plant - where you already have the fence.

But if you plant broad-leaved trees, that have crowns mostly above fence height pretty much all of these will grow much broader than 30 in. across.

So really we are back to something like a trellis with vines on it.