Maybe. The cable pull ratio will be the same, so if the Tourney worked with your shifters, the Claris should should mate with your shifters and index properly as well. But the 'SS' designation means you're talking about a short cage derailleur, which won't be able to handle big cogs on your cassette/freewheel or wide-range gearing like you might find on a bike equipped with a triple crankset.

To give you a definite answer, we'd need more information about your bike's gearing. How many speeds? Number of teeth on the big and small cogs? Single/double/triple crankset? How many teeth on the smallest and largest chainrings?