Removing a broken faucet aerator
Yes, you can unscrew and replace that aerator. Lucky for you, it appears to be a very common size and should be available at any hardware or plumbing shop (bring it with you).

The part you unscrew is the aerator body itself, the chrome part. Sometimes they are stubborn; you may have to get at it with pliers. I have even had to use destructive removal force on them on more than one occasion.