Finding a replacement faucet spout
You might get away with unscrewing the spout, cleaning the threads on both the spout and faucet with a brass brush (just to clear any accumulated crud, especially if you have hard water), wrapping the threads with thread tape, then tightening it back on.
If that doesn't fix it, odds are good that you'd have to replace the whole faucet. I'm not sure where you're located, but that type of faucet isn't common at all in the US and wouldn't be available at a large home-improvement center type of store. You might be able to find something similar at an actual plumbing supply house. They may have something in a commercial line that would fit. If you go that route, either remove the faucet from the wall and bring it in with you, or take good pics with a measuring tape across the top of the plumbing stub-outs so they can help you find something with the right spacing.