Are the old and the new the same species of wood? Most stores have a color chart for their stains on oak and pine, usually not much else. Tell us about your wood

How perfect do you want to get it? Assuming the wood is the same, matching stains exactly can still be quite difficult. The old wood wood be discoloured with potentially years of sunlight, dirt and oil. You may have good luck sanding the old wood and then staining both old and new with the same stain. Otherwise there are people who are extraordinarily good at colours and colour matching (I'm definitely not one). The best ones would probably be working in furniture repair/ antique refinishing near you - perhaps ask one for advice/ pay a few $ for them to visit (or bring them an old & new stair piece) and make some suggestions?

I just went through this same thing,the cabinet had old growth oak face and the customer wanted the new oak(facing on 2 new shelves)the same color as the old, it took 3 different stain colors to make a close enough match.

If you can,get more than just one color,you can never make the match with just one.I am fortunate to have close-outs and mis-mixed stains from our local Sherwin Williams,I have probably 35 different colors to chose from.It does take a little mix and match but you can make it close enough to pass a quick inspection.