The chrome pipe is the tailpiece from the sink (or it may be an extension of it). There should be a nylon or rubber gasket underneath that chrome nut that makes the seal.
If this is a new sink, it appears that the old faucet and drain were re-used? That chrome pipe looks rather rusty and may not make a tight seal.
It appears from what little I can see from the photos that the new sink is a bit shallower than the original and now the tailpiece doesn't quite meet the PVC P-trap. You need an extension for the tailpiece. That will require cutting the tailpiece back and adding a 6" PVC or chrome extension, which will also have to be cut to correct length.