Refinishing wood: Should I use wood conditioner after light sanding before staining an old desk?
I have found that wood conditioner is unnecessary for harder wood species. The primary purpose is to help reduce blotchy spots due to uneven stain penetration, which in my experience is prevalent with soft woods.

Previously finished woods may be less susceptible to blotchiness, depending on how thoroughly the wood was sanded. Conversely, less than complete removal of existing finishes can itself cause uneven stain penetration.