You can apply a thin layer of wood putty. Repeat until filled. If it is coming unglued, use wood glue and clamp it in place. You may be better off removing and putting new in place.
If you have the missing pieces of veneer, just glue them in and clamp for a good adhesion. If the pieces are missing, you can use wood putty, let dry and sand when smooth. It may be necessary to remove the veneer and start fresh with new veneer.
Take item or picture of close up of veneer to Craft shop. They sell veneer and will be able to sell you a book on how it is done and supply the tools etc.
Veneer is hard to repair you could glue down what’s there and use wood fill to fil in what’s missing . Or remove all the veneer by wetting it it will buckle and you just take it off there will be beautiful wood underneath.
Here are several ways
https://www.hometalk.com/search/posts/?filter=repair%20veneer
How to Repair Wood Veneer on Furniture
https://www.doityourself.com/stry/how-to-repair-wood-veneer-furniture
If it's just lifted, you can squeeze some wood glue under it and clamp it until it dries.
here are some ideas Ronnie
https://www.youtube.com/watch?v=YPO2ChfxJmU
https://salvagedinspirations.com/how-to-fix-peeling-or-chipped-veneer/
You can apply a thin layer of wood putty. Repeat until filled. If it is coming unglued, use wood glue and clamp it in place. You may be better off removing and putting new in place.
If you have the missing pieces of veneer, just glue them in and clamp for a good adhesion. If the pieces are missing, you can use wood putty, let dry and sand when smooth. It may be necessary to remove the veneer and start fresh with new veneer.
Take item or picture of close up of veneer to Craft shop. They sell veneer and will be able to sell you a book on how it is done and supply the tools etc.
You can glue the veneer if it is still in tact. You can use Bondo, heavy duty wood filler to fix open spaces. Overfill, then sand down and paint.
Depending on how it is damaged, you may be able to repair using a good bonding glue.
I have had luck using a heat gun to remove the old veneer then sanding and painting the top of the furniture.
Veneer is hard to repair you could glue down what’s there and use wood fill to fil in what’s missing . Or remove all the veneer by wetting it it will buckle and you just take it off there will be beautiful wood underneath.
This site has quite a bit of good info on repairing wood veneer
https://homeguides.sfgate.com/fix-table-veneer-cracked-bubbling-42883.html