It's possible to re-finish it, but the missing veneer on the front edge is a problem that would require the services of a really good furniture repair person. It might require removing a strip of veneer all across the front edge and adding in a uniform color piece since you can't make little patches that will blend in well. And the fact that the veneer replacement would be on a surface that is curved in two directions makes this particularly challenging. It could cost more than the piece is worth if you want it done right.