The Westies are an Irish-dominated gang who play a prominent role in two episodes, "Sucker Punch" and "Headhunters", although they're first mentioned in "Home Is Where the Heart Stops". In that last episode, Evan Mitchell talks of his Westie pals when asked for an alibi.
In "Sucker Punch" we meet their leader, Finn Rourke, a man with barely veiled contempt for law enforcement, but who does have rules of his own. One of those is "no drugs on my streets", and to that end he sent his chief leg-breaker, Jackie Coonan, to "have a word" with dealers looking to muscle in on his turf. Jackie's corpse kicked off the episode, and led Beckett much closer to solving her own mother's murder. Later, it is revealed that Rourke knew who really killed Jackie, but since he considered the killer to be untouchable, he blamed a rival gang instead.
"Headhunters" revolved around Castle's new muse, gang Detective Ethan Slaughter, a loose cannon firing off shots in the direction of the murder of "Glitch", the useless son of top Westies' enforcer Brian Reilly. Glitch was found next to the heads of three Jamaican gang members in a bag, leading Slaughter to conclude he was trying to prove to his father that he wasn't a screw-up after all. Slaughter and Castle detain Brian and another Westie; with Castle having to man-handle the second gang man on his own, and earning a bloody nose for his efforts.
It turned out that a Mexican drug gang was attempting to break into New York. They needed to beat down their competitors, and had manipulated Glitch into triggering a gang war between the Jamaican gang and the Westies. Realizing what had happened, and that Glitch had made a mess of things yet again, Brian had, in his view, no choice but to eliminate his son himself.