Connor was an Irish hitman employed by Carmine Falcone.
Working with Penguin
Oswald Cobblepot arranged a meeting between himself and Connor, as he wanted to put a hit out on Sal Maroni. Although originally reluctant to do so, Connor gave in, after Cobblepot brought up the fact that Connor stood second to Victor Zsasz, and that if he brought Falcone the head of his enemy, he'd get first dibs on all contracts. Connor and his associate later confronted Maroni at Lidia's, pointing a gun at Maroni, only to find out the gun was empty when he attempted to shoot him. Connor was then killed by Tommy Bones, and his decapitated head was sent to Falcone, starting a gang war between him and Maroni.