What if we planted trees along the edge of a desert?

It is being done now in the Sahel, it is succeeding slowly.

https://youtu.be/htgtuAWcWMQ

I suggest planting desert adapted trees such as date palms or plant aloe and cactus that can store water. You have a great idea.

it is succeeding slowly.

In some deserts yes it can be done. Much depends on how deep ground water is. Trees can be planted then watered till the roots go deep enough to reach water. This could be done in much of Arizona, New Mexico. Were there is a high water table. Texas. But were water is deep no. Then what do you do with the trees? Most are a soft wood for this. Slow growth. Now if you can develop a grass were the roots go down 20 to 50 foot. You are onto something as cattle land.

Without irrigation, the trees will whither and die.

With irrigation, you will have a windbreak. The desert will still be dry.

When you say "re" forest, that suggests that forests were there before which isn't always the case. It seems to be popular to favor a forest over environments. I have lived in South Dakota at the edge of grasslands and the forest. I usually preferred the forest but I still love the grasslands. I lived in Phoenix (Mesa) for a couple months and grew to love the desert there. There are lots of cool plants and animals in that environment. Rather than necessarily planting trees, I would support protecting the natural environment in most cases, whether it be desert, forest, grassland or whatever.

yes

The soil (or sand) of a desert is not fertile enough to support plants; when they do, its only for a certain subset of plants that do adapt to such soil. You could probably plant a number of date palms all along the edge of a desert (like you say, choose trees that thrive in that climate) but date palms aren't exactly known for their carbon absorption capabilities. Its futile if carbon sequestration was your reason for such an idea. You haven't mentioned why you would like to do this. "could we reforest a desert" yeah, probably if we paid enough attention, time and money towards it, but a desert is a homogeneous self-balancing eco system, and does not need to be "forested". The world has enough forests, with their accompanying climate. Its those places that need to be reforested, and not entirely different eco systems that don't support forests.

not necessarily

Don't think that would work, dust storms would cover them and the whole point of a desert is that there is NO or little rain, they would just die.