You can use Goddard's 'Silver Dip' to remove the tarnish by immersing the keys into a non-metallic tray filled with it (two jars will be enough), then rinse the keys thoroughly and polish with a silver polishing cloth.
How do you clean a silver clarinet?
Individually wipe all sides of each key piece with a silver-polishing cloth (usually sold for kitchen utensils). Only wipe each piece enough to remove the visible dirt and tarnish, and do not wipe the cloth on the tone hole pad. Reattach each key piece to the main body of the instrument as you finish cleaning it.