Barbs, Tiger Barbs especially, set pecking order in the tank.
Have you ever watched them, with their lips locked together, swimming in a tight circle? They're sizing each other up.
I suspect this is what's going on.
How much smaller is the new barb than the other three?
What size tank are they in?
Does it have a good place to hide? You might consider putting a couple of (properly washed) small flower pots in the tank, if not.
They're nippy fish for sure. As long as he's swimming around and not cowering in a corner, I don't think you've got a problem. Just like kids, they'll work it out, then when one submits, they'll be best friends.