This is a Gravina Crime Family mission.
"It's your lucky day! A good friend told you where to find Gravina's consigliere, an old fart called Ettore. Ettore is the real brains of the Gravina outfit. The problem is that those brains are in his head. They'd look better on a wall. Take care of him."
Once you activate the mission jump back in your car and head toward the moving marker on your mini-map. Ettore will be riding in the back of a limo along with three of his goons. You'll want to bring along a decent sized car to make stopping him easier. You can pull ahead and cut him off or just ram into him a few times and they'll eventually stop. If you continue to follow, they'll just keep driving around the city, but if they have to stop for any reason they will jump out at that point.
However you get them to stop, they'll all open fire with their SMG's immediately. They're pretty decent shots so you'll want to get out and find cover quickly. Once you kill them, make your way back to the safe zone in Little Italy to end the mission.