I don’t have any specific recommendations for software or services, but I do have a couple general thoughts on this problem

How many pieces are missing and how ornate is the set?

If you have at least one of every piece the easiest course of action is probably to 3d scan them. A scanner is probably a bit pricey to buy just for this one project, but if you ask around you can probably find a hobbyist or makerspace that will let you use theirs.

If you can’t find a scanner, as long as your set isn’t too ornate, most chest sets are probably pretty easy to model for the most part. Except for the knights which are of course horses which are a weird irregular shape, most chess pieces are essentially cylinders and cones of various sizes stacked on top of each other. With a little quality time taking measurements with some calipers and some youtube how-to videos, you could probably learn enough to make a pretty decent model pretty quickly.

You might even be able to carefully trace your pieces onto a piece of paper or maybe use a contour gauge to do the same, scan that tracing into your computer, and create a 3d model from that profile. Heck, you might even be able to just take a picture of the pieces then trace them on your computer.

It’s been a long time since I’ve done any 3d modeling personally, but something like that is a feature in a lot of software I’ve used.

Then you’d just need to add some details- a slot cut into the bishops hat, some crenulations at the top of the rook, a cross on top of the king, etc. which should all also be pretty straightforward to model

Again, if you ask around at makerspaces and such you can probably find someone willing to take up the challenge or help you figure out how to do that.

Of course if your set has a lot of textures and details you wouldn’t be able to capture them that way, like if your pieces have a face or otherwise aren’t rotationally symmetrical, or the rook has a brick pattern, etc.

And if you need to model the knight, that’s going to take some more advanced modeling skills unless it’s a really simple and kind of abstract horse.

If you are missing pieces entirely, unless you can track down another set to use as a reference, you’re going to have to recreate them from scratch. You can take some styling cues from the other pieces- like the bases are probably all pretty much the same, but beyond that you’d kind of have to work off of memory and eyeballing them.

EDIT: When all you have is a hammer, everything looks like a nail. I was thinking about good ways to recreate your missing pieces by 3D printing so I kind of forgot to consider other techniques

Again, assuming you have at least one of each of the pieces you need, make a mold and cast new ones out of epoxy or something.

Also, again assuming no detailed textures, except for the knights, most chess pieces are almost perfect lathe projects. There’s some really cheap tiny lathes to be had on Amazon that would probably be up to the task of turning a chunk of plastic into a chess piece.