The eastern segment of NY 24 begins at exit 71 of the Long Island Expressway (I-495) in the Calverton section of Brookhaven just east of the former Calverton station. NY 24 proceeds eastward along Edwards Avenue, concurrent with County Route 94 (CR 94) before changing monikers at the corner of South River Road. NY 24 bends northeast along Nugent Drive as a four-lane arterial through Brookhaven. NY 24 and CR 94 cross through Peconic Bog County Park, crossing into the town of Southampton. After leaving Peconic Bog County Park, the routes bend northeast along Nugent, paralleling the Peconic River past the Suffolk County jail and into a traffic circle just south of Riverhead.